Jazzmaster or Blacktop Telecaster?

So I've got an Epiphone Casino, and I've been wanting a solid body guitar, and it's come down to a Blacktop Tele and a Jazzmaster.

I've got a budget of about 800 Euros, so I'd be going for the mexican versions(Though I've been thinking of replacing the bridge pup of the tele with a red dually lace sensor).

I'm mostly into playing Beatles, Radiohead, REM, Black Keys, Blues improv and Muse(not very fun on a Casino lol) stuff.

Any info I should know going in to this or suggestions?