I learned and now teach both together... I find they reinforce each other.

Theory can get pretty dry, so playing your way through it makes it easier. I also like to understand what I'm doing rather than follow instructions... so relying on TAB alone wouldn't do it for me (and it wasn't very available when I started).

I think my students are the same.... they become that way anyway. As Kevin says, for some things the theory / reading notation element can be pretty much essential. I'll be honest, I didn't thank my teacher at the time for all the theory stuff, but without it I wouldn't be capable of some of the things I do.

Believe it or not, once you start 'getting' the theory element it makes the rest easier. Only thing I'd say is, if you start learning music theory go slow but persevere unless you are very loss. So much of it is reliant on other aspects that the reason you might not quite 'get it' could be on the next page of the book...

It's important to stay engaged in it though, so if it ever gets boring go learn a song... Also bear in mind that some of the greatest players don't read a note, so don't dispair if it isn't for you... :)