First of all, as far as compatibility goes, I think you're right, unless if Nintendo states otherwise, Switch games are compatible with every version of Switch they dish out. That logic goes for all consoles since the 90's when the PS1 (Sony) and N64 (Nintendo) were the only big boys on the block during that era.
Secondly, you need to ask yourself if you want portability or home entertainment. Think of it this way:
Portability = Switch is the option for you. PS4 has virtually no portability, so the clear winner for this is obviously Switch.
Home entertainment = You certainly cannot go wrong with the PS4, or at least with the BluRay/DVD optical drive, compatible with Netflix, YouTube and other media apps that allows you to watch TV shows and movies on, and so forth.
Video game wise, they're both good and can't really lose regardless of which one you had gone with, both have their good selections of games and such, so there's really no real answer to this as everything stated is just purely opinions and favoritism towards one or the other.
To answer your question though, I personally would go with the PS4 though.