Yeah, it COMPLETELY depends on the application.
If something fits in RAM, then the faster the better. If it doesn't fit in RAM, then you get a kick down in speed like 100x as it has to hit the hard drive.
So load up whatever you think the max you'll have, then check the physical memory used. If that amount is close to or greater than 1024 MB, then go for the 2GB, if it is significantly less than 1GB, then go for 1GB.
For just gaming, 1GB seems to be fine (for now). I play a lot of BFV and UT2004. If I alt-tab out and check Task Manager for physical memory used, they are both in the 600-700 MB range, BFV a little higher than UT2004.