I have both. My first Fender was a '57 RI strat. It took me about a year to really learn to play it. Strats & Teles both I believe challange you as a player. You have to "learn" how to use the switches, the tone controls, and of course the Neck. I have always been more of a Strat guy. I have many HB guitars as well, but I tend to lean strongly to the Strat although the last few weeks I have been playing both of my Teles. They are crisp by comparison to a Strat. They can be very bright. Almost dog wistle bright. I feel fortunate that both my Teles do not have that harsh sounding bridge PUP. The neck PUP in a Tele can give you some suprisingly good Jazz sounds also. Lew said it also the middle position on a Tele is one of the best sounding Rythum sounds ever!
Alot of guys overlook this and the stock neck & stock bridge of a Tele combined really is one of the best sounding rythym sounds ever. You'll hear it all over Pretenders CD's. If you replace the Tele neck pickup with a "hotter", "better" pickup, like a Strat pickup or humbucker or P90, you'll lose that tone.
I have a tele which I love. I prefer the "bite" of a tele to the strat. As mentioned previously, tone wise, I think rythm sounds better on the tele too. I remember years ago when I played a strat for the first time, I kept turning the volume down with my little finger accidently until I got used to where the volume pot was located. I like both axes though but put the tele ahead for tone quality.
When I think of a strat I think of nice, clean, smooth tones and it does it very well. I like the tele for it's bite, twang, and kind of in your face tone. And the bridge and neck combo is sweet for rythym. I have a tele and am wanting a strat when I get some money. I think everyone should have at least one of each in their bag.