So what is the difference between them? I can imagine that Power Bash can work as a power attack seeing that you can perk it to do 5 times normal damage, but what would make anyone take it instead of improving power attacks for his weapon?

Power bash leads to another perk that let's you disarm your opponents when u power bash them... And some other perks I think.

Power Bash is more......Powerful.

He's asking what's the point of it if you could just improve your normal Power attacks

I didn't think there was a normal bash...I think you need the perk to bash at all.

there is a normal bash, it more or less just staggers the opponent some. Power bash does some extra damage.