I just got Fallout 1&2. Fallout 1 was choppy to the point of frustration. Fallout 2 was a lot better.
After some trial and error, I found that if I delete ddraw.dll from the Fallout directory, the choppiness seems to go away, and everything else works just fine.

It's even in the FAQ i think. Interesting thing though that I had to restore the file to get rid of black screen problem that was happening several times a minute...

many people say that is helps to delete it. What does the file do for the game in the first place.

It's a DirectX component, most likely a much older version than what's installed on gamers' computers system-wide. The reason it's there is probably the one tomba4 mentioned: The game has a tendency of occasionally painting the screen black and you have to make things visible again by rubbing the black away with the mouse cursor. I think this happens on newer DirectX installations but not when using the older ddraw.dll. Unfortunately, while it may work for some, for others it may manifest incompatibility problems such as but not limited to: choppiness.

In the fallout 1 FAQ thread, Paul_cz may have found the solution to the blackouts:
He said, "Regarding the blackout bug - are you 100% sure that you do not have any program running in the background, like ICQ or QIP or RapGet or Skype or something?
Because I never had a blackout, then I started downloading something via RapGet and started playing Fallout, and everytime a file downloaded I got a blackout.So it was caused by it taking over in the background.After I disabled it, I NEVER had a blackout bug again with my configuration."
It might be worth having a wee look to see if there are any of these programs running in the background.
EDIT: Also, Fallout 1 was very badly choppy for me when I first played it too. Weclock's FAQ said to re-name ddraw.dll and after this it has worked very smoothly.