Halo:CE It has the best campaign, the level designs were fantastic, the flood were exactly the way they should be, the Elites were tough as nails and even alone were considered a threat.
The multiplayer was great for LAN and the ideas were brilliant (riding shotgun on a tank).
If they remade it with updated physics and graphics it'd would be the best by far.
Halo 2 It's campaign was lacking in length and depth, the false advertising used before the game came out also made it a huge disappointment.
It's multiplayer was better because it was online, the ability to dual wield was great and most of the new weapons were great, although getting rid of the assault rifle was foolish.
It also made a few negative changes:
The Battle Rifle: The gun is fine but it should not put a sniper out of their scope as its range makes the sniper more or less useless.
It changed the view for passengers of vehicles to 3rd person which makes it easier but completely gets rid of any immersion.
Vehicles cannot be left while moving, if you are going full speed and choose to leave, the vehicle will slow to a stop first which is dumb.
Halo 3
The campaign was better than Halo 2's but was still too short and lacking in depth. The Brutes make a poor substitute for Elite's and with the exception of Legendary Mode provide no challenge at all.
It adds too many new and pointless weapons such as the Brute Spiker, Brute Spike Grenade and the Mauler.
The multiplayer maps generally speaking are too small and lack the fun of the tank battles from Halo 1 and 2.
You can no longer ride on a tank shotgun-style (apparently the characters forgot how to do it).
They force you to have all the map-packs to play any games modes apart from one or two.
I could go into much more depth but I shall only do so if asked.