WA vs WWP
From Worms Knowledge Base
Let me begin by saying that WA and WWP are essentially the same game. If you looked at screenshots, you wouldn't be able to tell the difference. WWP and WA have the same graphics, the same weapons, the same sounds, and the same terrain sets. So when making the choice between the two, it all comes down to the smaller features which add up to make a big difference.
There are a few things that WWP has which WA doesn't, such as a mission editor, a few "wormpot" modes like high-friction or super-rope, and more single-player missions.
But there are far, far more things which WA has that WWP doesn't. For a short list of the most significant features, see here. The reason for this is that WA is currently being updated. Dozens of updates have been released over the past two years, whereas WWP was last updated in 2003. The updates aren't set to end any time soon, either, and an awful lot more has been planned for the game.
Most people will tell you that WA also has a larger, and more active online community.