The story in Mass Effect was great in my opinion. It started out as saving some colonists and grabbing a team to stop an unknown threat, and the rest of the game was about finding this threat, what it was, and eventually defeating it. It felt like a real achievement defeating Sovereign, in no small part due to the fact that the entire Arcturus fleet had to engage it to take it down. The story here was more of an investigation, before getting a warrant to search a criminal's house, only to find out that the criminal is a full fledged terrorist and is planning to blow up the equivalent of the White House, the Pentagon, and all the surrounding area before getting his army to invade the US. The story also had a main antagonist that we often saw and interacted with, and who was an antagonist by flawed reasoning and indoctrination, and it is possible to turn him from this path (though he dies either way). It also felt like Saren was actively trying to disrupt your efforts, with either him or one of his trusted minions going basically everywhere you went for the main story and fighting against you.
Mass Effect 2's story was more akin to light reading IMO. You spent the majority of the game gathering a team, with occasional skirmishes with the main threat. Once you finally have your team collected, the real story telling begins, however, this is a small portion of the game compared to actually recruiting the team. Every member has loyalty missions (However, many of them short and offered little insight to the character beyond what you can learn by talking to them), your team infiltrates a dead reaper to get its IFF, and you invade the enemy base. The final boss felt pathetic. A creature that took me an entire fleet to take down in ME took me two or three shots from my heavy weapon to kill, dependent on the difficulty. The story here for me was more akin to going to the crimescene to get evidence, finding the criminal there, calling for reinforcements while the criminal gets away, then chasing the criminal to their base of operations and taking out them and the car bomb they were building for a rainy day. The antagonists in this were both the collectors and the reapers, and didn't really have a face like Saren did. They also didn't feel like they were trying to stop you, appearing only rarely to invade a planet or set a trap. Most of the time your opposition was mercenaries that had no relation to the Collectors.
The inventory system in ME was cluttered and did not work, whilst the inventory system in ME2 was almost non-existent. The only 'inventory' you had was the ship one, and everyone could get an infinite amount of anything from there. People complain that the weapons in ME were the same as each other, but each level just kept getting better, and for the 'good' weapons (The ones that trumped the rest in every stat even though they were a lower # level) this was true. ME2 however, is no different. Each assault rifle shoots, and we take the games word that the one we have now is better than the previous one (Well, we don't take its word as such. We trust that it is seeing as we found it later in the game). There aren't even any stats for the gun so we can see how good it is. We just get a short backstory for it. We have no idea of damage or fire rate, unless we test and measure it ourselves.
There are also no weapon mods in ME2, which allowed you to specialize your guns for different types of fighting, and the only ammo mods were abilities I had to spend points on.
Armour was actually pretty good in ME2. You had parts of armour to build up a whole custom suit, specialized to what you wanted it to be. In ME1, the specialization came from armour mods, and you had a ton of spare armour sitting in you inventory most of the time.
Combat in ME was clunky, and usually quite dull until you put it on a higher difficulty. You sat behind a wall, popped out of cover and shot. That, or you ran in circles around an enemy and shot, relying on the fact that you had more HP then them. Both are rather dull in ME, staying in cover is rarely fun and when your characters move as slow as they do in ME, running around the enemy in circles is rather boring too. However, the game did strike a balance of needing to do both to get past some areas. In some places, you would need to take cover or else you would be killed by the enemies (When the assassins attack you whilst you are looking for Harkin), and others where staying behind cover was not advantageous, and melee enemies or rocket trooper splash damage would end up taking you out if you stayed there too long (When fighting Rachni, Husks and at a certain point on the mission to get Liara). There were also a lot of sections that let you do whatever style worked for you. Abilities were quite well done for the combat sense, you could have fun 'Alpha Strikes' or tactically line up a few abilities with the right timing for some fun effects. You could also just use one ability if you wanted to.
In ME2, the vast majority of combat is done behind walls (Every time there is a ranged enemy fighting you), and you have next to no health. The low health and faster speed of Shepard help to make it less dull, but after my 42nd hour of sitting behind a wall shooting, it was really just dragging on. There were occasional times when you would leave cover and run around the enemy attacking them (When you were fighting all melee, or a vast majority melee enemy force), but most of the time it was just move from wall to wall, or sometimes (When fighting Praetorians) moving from wall to wall, oh wait, I already said that. Abilities were poorly done from a combat perspective for ME2. I think it was meant to add some level of depth to the combat, 'pick the ability you use wisely, you won't be able to use another for a while', however it didn't with only one or two abilities getting attention. The individual Class abilities were quite fun to play with however, and I especially liked the Vanguard's charge.
The different types of armour in ME2 were also an interesting concept, and whilst it didn't feel like it completely worked for me and I would like to see an improvement on it, I cannot think of what areas I believe it needs to improve in. The ammo system in ME2 was a welcome add in for me, and ME had felt rather odd for the first part without it.
ME gave you an incredible amount of abilities and skills to invest in when you leveled up, however there were too many and many rarely got used. Weapon abilities and armour abilities were pointless additions, however they gave some much needed bonuses by end game.
ME2 strips a lot of this out, yet still has the problem of a lot of abilities being useless most of the time thanks to the multiple armour type situation. I do like what they did with the skill specialization at the end.
Experience in ME was rewarded for doing things, and the more things you did, the more experience you got. Not too much to complain about, unless you were hoping on stealthing your way through the mission. If you want to talk your way out of combat, your not left behind in XP either though, as you get the same amount of XP for talking your way out of something as you would have for killing all the enemies, and usually some Paragon/Renegade points to boot. You would get XP for finding out new things about the world (Interacting with certain objects that got you codex entries) and for opening locked chests.
In ME2 you got XP at the end of the mission, not reliant on what you had done. In many ways, it didn't need to be for ME2 as you had to kill or talk your way out of killing every enemy anyway, but things like opening locked chests and doors instead resulted what I think of as the real XP for ME2: Credits. Once again, not much to complain about here, as the level design makes it so this would be how it would work out anyway (except the locked doors/chests).
Credits in ME1 were extremely common, and you could easily get the maximum amount by the end of the first or second off citadel mission (Courtesy of the inventory overload). If you wanted something, you could by it and 100 other copies of it, and still have enough credits left over for your long service holiday to the other side of the galaxy.
In ME2, credits are a rare and valuable commodity. You need them to pay for fuel, to get probes for planet scanning, armour pieces and to buy upgrades for you and your team, basically the effect of the passive abilities in ME. I actually preferred this approach as it made me think about my purchases, just so that I could buy everything.
Morality in both games changes very little, and is just as pointless until ME3 (and may still be redundant even then, though I hope they do something good with it).
Level design in ME was a lot of cut and paste areas for side missions, a few designed areas for main missions, and a few barren planets. The cut and paste areas had the internal maze of boxes changed up most of the time at least, but were still glaringly obvious. ME also had a semi-linear to non-linear approach to its levels as well. On the planets, you could go anywhere except outside the boundary zone, in the designed levels there were usually more than one way to get somewhere, and only in the cut and paste levels did linearity actually take full control. This lack of linearity, the ability to avoid some enemies completely, or to hunt them all down, to explore as little as need be, or as much as you could, was something I quite enjoyed from ME.
In ME2, levels were completely linear except for in hubs, with only one path to the exit. There were side passages, usually dead ends, but sometimes allowed you to take a different path somewhere. However, you would never miss an enemy (Or very rarely at the least). The levels themselves however, were at lest not cut and paste, and had actually been designed properly.
Conversations in ME and ME2 barely change at all, except for the interrupts added in to ME2, which I quite enjoy playing with.