That depends.
A lot of factors play into frame rate performance. The great thing about the 9800 pro is that you can turn on Anti-Aliasing and Ansitropic filtering to get rid of jaggies and other 3D artifacts, although at a performance cost. Check out this article on filter applications. There are a few comparisons of games with and without filtering. Also, some games the filter results are better than others. Anyway, with the 9800 and strong filters on, it is still a bit faster than the 4400 without. But with out those filters on or if both have the filters on (Apples to Apples), the card will range from 33% to 200% faster (averaging around 100%), depending on the game. Really the best way to look at it is to look at some benchmarks. Check out this article at Tom's Hardware, it is pretty extensive. They test a lot of games with a lot of cards. You can probably pass over the pages and pages of intro text if you dont want to get into the techincalities.
BTW dont feel like a Noobie on this. To keep track of the enormous number of chipsets, versions and revisions is impossible. I have trouble and I have a lot of time on my hands these days.
D>M>