Well, higher vRAM amounts don't generally make much difference in current games at resolutions of 1920x1200 or lower. If they're the same price then why not get the 2GB edition, however MSI is much better than any Palit.
The extra VRam will only be useful in two scenarios: 1) you are using multiple monitors, 2) you are concerned that games in the future will require much more graphics memory than they do now.
I'm going to say that the extra memory is not a concern at your resolution, and it will be a long time before games get that graphically intense (in fact, the current trend is for them to be less graphically intense), so go ahead and get the MSI card.
Firstly, 1920x1200 DOES benefit from the extra ram especially when cranking up the goodies. Secondly, DON'T waste your time on the 2gig Palit card. I had one. The VRM gets too hot and makes the card spit and sputter. RMA'ed.
If you find a need to get a 560 go for the over clocked ( 950 ) Gigabyte card. A friend of mine runs 2 in SLI and they're pretty good.
I agree with Swifty's assessment. To get a clear picture of the 2gb vs. 1gb issue, all you need to do is look at a review of the 6950 1gb card. Like this conclusion from Guru3d, which I was more or less quoting:
"So first off, did you guys check the difference in-between the 1GB and 2GB 6950 versions as well, yeah ... the results are nearly NIL. The added benefit of an extra full GB is excruciatingly hard to measure, even with all games setup with the best image quality settings, hefty shaders and massive textures. The reality is that for 98% of you with today's games 1 GB is absolutely sufficient.
Why would you opt 2GB you might ask yourself ? Well, there are several scenarios, first off very simply, being future proof. In time games will be more demanding when it comes to things like texture requirements. But a more important reason would be multi Monitor gaming, thus Eyefinity. It's there where you breach any foreseeable limitation versus resolution and that's where the extra memory can come into play."