...by running a game off a memory stick instead of a UMD? I like having a box and physical disc when it comes to movies and games, but if I can save some battery life by not using the UMD drive, maybe I should get the digital copy instead. Has anyone compared UMD and UMD-less games such as Patapon 2 and Jeanne D'Arc to get a clear indication?

I find it a lot better to have it through download only. Meaning you have your whole game library on one device and you can play whichever game you feel like at that moment without having to swap discs. Also the UMD loading noise is gone and I think games load a lot fast too (maybe it's just mind tricks!)

As someone who has run data off a memory stick for years on the PSP I will say it saves not only loading time, but battery power =] I'd say a good hour and a bit extra usage.

Definately a fan of using the memory stick wherever possible. 

How many GB of space should my Memory Stick have? I currently have one of 4GB; but I thought that maybe it won't be enough. Afterall, a UMD stores around 1.7GB, although I don't think every game is that big. So, is 4GB enough, or do I need more?

You notice it when you're playing a download game. The UMD just sucks power.