the only obvious major difference is double the storage capacity and double the ram. the extra ram gives you a lot more headroom in multitasking, gaming, things like photoshop, etc... its more so for power users or gamers. with me, id rather have more than enough and not need it versus come a time when I need it and don't have it.
I have a 128gb pro1. with steam games and even apps/games from MS store, it doesn't take long to burn through the storage space. These apps and games have some large file sizes.
plus the higher model would have more resell value should you choose to sell or upgrade down the road. its more futureproof per se. id say if you have enough, get the 256gb model. but if you know youd never use that much storage or aren't a heavy gamer or artist or use VM, then save the cash and add some cool accessories to your 128gb version.
now with recent price drops by MS for the pro1, I could've got a 256gb pro for the same price I paid for my 128gb version...smh I need the extra storage. I know if and when I get a pro2, it has to be the 256gb. I need the storage and want the extra ram.
Comparing gaming benchmarks with people who have the 4GB ram models, it looks like performance between them is more or less the game in games. If you want to use Photoshop or go big on multitasking then I guess 8GB could help. Personally I got the 8GB model because I do game development with Unity, Visual Studio, and a bunch of other apps open at once. I also figured I might as well go with big ram because I won't be able to upgrade it later.
Though if you don't find yourself in need of a ton of storage and don't use any apps that guzzle memory then the 4GB/8GB models are going to be the same for you.