I played Fallout in the order they were released, just not anywhere near the times they were. If that makes sense.
See, I wanted to play Fallout 3 pretty badly, but couldn't run it, so instead I played Fallout 1 then 2.
It's clear that Fallout 1 & 2 were great games for their times, but nowaways they've simply aged to the point where it detracts from my enjoyment - for example, the clunky inventory system, annoying bugs (I did install user-made patches which helped a lot), and how some X was simply BETTER than Y. X and Y could mean equipment, companions, SPECIAL/skills/perks/traits, etc. which translates to so much missed opportunity in the form of varied gameplay experience if they had been implemented and balanced better.
I then played Fallout 3. When you compare how good Fallout 1 & 2 were against other games that were out at the time, and Fallout 3 against other games that were out when that was released, they're probably pretty much the same in terms of how good there are comparatively.
However, Fallout 3 is simply new, and with that comes a lot more enjoyment - better graphics, voice acting, better balancing of SPECIAL/skills/perks, easier inventory management, and other assorted luxuries that come with modern video games. The raiders did piss me off though, because of how common they were, how they didn't have any redeeming qualities, moral choices, quest lines, interactable NPCs, or anything past "BAD GUYS LOL".
I have noticed, however, that while Fallout 1 & 2 could be extremely frank in terms of the darkness of the post-apocalyptic setting (various criminal underworlds, etc.), Fallout 3 simply skipped out on a lot of it. There isn't much swearing, slavery outside of Paradise Falls (and they don't seem too bad off compared to previously), or any of the darker stuff that was prevalent in Fallout 1 & 2.
No! I'm not some twat who enjoys stuff like that simply for the fact that they're there and shunned by society and me liking it makes me super cool. I mourn the loss because it detracts from the atmosphere: I don't personally like using the word fuck to punctuate my sentences, but it does detract from immersion and the gameplay experience where not a single low-life scumbag does that in Fallout 3.
Also, as previous posters have noted, Fallout 3 lost a lot of the quirky humour that defined the previous games in the series. That does suck.
All in all though, I'd still rather play Fallout 3 over the classics right now, because it's simply newer, and generally newer translates to better, as it does in this case.