I've since seen two episodes of each, and I think I'm going with Mushishi. Beck was fine and all, but it was just a little too cheesy. I'll probably continue watching it sometime, but for now, all I need is Mushishi.Beck is good, but focuses more on drama than action so if you're not too into less actiony anime it's probably not for you. Also the engrish singing kinda hurts at times. If you can find the English version the voice acting is pretty good.
Mushi-shi is more episodic, but definitely worth a watch. It has a slower pace than 90% of the anime out there, but in this case that's not really a bad thing.
Oh, don't worry, I couldn't care less about whether an anime has action or not If it's good, it's good.Beck is good, but focuses more on drama than action so if you're not too into less actiony anime it's probably not for you.