GTX 780M 4GB vs. GTX 880M 8GB

Will the additional 4GB's on the 880M make a difference in gaming?

I'm trying to decide if I should wait for an Alienware with an 880M in it or just go for the 780M Alienware 17 that's already out.

No, it shouldn't be a problem at all, unless you're using multiple monitor.
The 780m is more than enough for your laptop.
You can even scale down to GTX 770 and save some money, you will not notice the different(unless you have super sensitive eyes)

Nope. Your monitor on that lappy is what 1920x1080 at the most? 3GB is fine... 4GB is PLENTY, 8GB is overkill.