Precision Bass vs Jazz Bass

So I've been thinking of getting myself a new bass guitar. after I save enough money by not eating for a month. I've used a couple of different models already but all of them were just borrowed so I haven't really checked them out in detail. Usually I just make sure I get the best sound from them.

Looking up stuff online, it seems there are two definitive models where you can start from and I found this video that pretty much compares the two.