Hey Malte, I’d say either of those basses will probably work fine. Usually Fender instruments have higher quality hardware etc. than the Squier line since Squiers are meant to be “budget” instruments, but because Fender/Squier cranks out so much gear, it’s hard to say anything as blanketed as “Fender is always better than Squier.” I’ve played some great Squier instruments.
So since you can’t play the two and make up your mind that way (which is ideal), I’d say pick the one you like the paint job on the best. 
And there’s a lot you can do with string choice to tweak the exact P-bass sound you’re getting. Like if you want the sound in that first video, I’m guessing flatwounds with a pick will get you there. And flatwounds + fingers = the James Jamerson / Motown setup (with some foam in the bridge for full effect).
Hope you end up with the P-bass of your dreams!