It really depends on what kind of experience you prefer. I much prefer vanilla Android, and the ability to customize things the way I want to (instead of having to use a manufacturer skin), so I'd go for the GPE.
what software advantages does sony stock over GPE? Like only thing I saw that I like is the battery saving mode where i can shut everything down except a handfull of apps i want to have access
i don't think there any software "advantages" over GPE, there's just more software, that you may or may not want, with GPE you can get any battery saving app or mod/kernel you want. and yes you can side load.
ive tried side loading the walkman app on another phone but it said package file is invalid, what am i doing wrong. when you side load a app is it always supposed to work, regardless of your os version or no matter if it says that app is exclusive to a certain phone type
if you're able to sideload the same apk on one phone but not the other then maybe carrier or manufacturer is restricting it, might have to install a custom rom. developers can also specify which versions of android are required for their apps to work.