It would help if you told us which laptop model it was. However, most likely, it'll work with a 20gb hd.
MOST 10gb HD's are 9.5mm thick. Both of those 20gb drives you mentioned are 9.5mm thick as well. That's good.
Personally, I prefer the DJSA220. It has a higher density than the toshiba and tends to be a bit faster.
Here's the problem. SOME people with DJSA's report having a problem with loudness (I've had many ultra quiet ones and one that makes a high pitch whine). Others have had problems with HD death (though no more % wise than other manufacturers).
One thing to keep in mind, all 9.5mm drives are about 4200rpm. It's not until you reach the 12.5mm thick drives that you get to 5400rpm (and a reasonably good jump in speed).