[FrankHudson]

For several decades my answer would have been quick and sure: Telecaster.

My answer now would be long and complicated, but if forced to make a theoretical one of the other choice, it'd still be a Tele. And the market now has multitudes of designs with various features that still get recognized as a Strat or a Tele, even though they don't duplicate the original models or their classic vintage specs that usually came a few years after introduction. I'll speak below as if a mid 50s Tele or mid 60s Strat design was the thing being discussed.

IMHO, the Telecaster is more versatile. The fixed bridge is a blessing for alt. tunings and certain kinds of left hand vibrato. The neck pickup has a distinct woody tone when played clean (I've often watched Bill Frisell play a whole set on just the neck pickup), the bridge pickup position has more sock and beef in my favorite examples than a classic Strat, and even those examples that seem overly bright respond to the most useful tone control in any classic design. The two pickup position is hum-cancelling and picks up a lot of string vibration range without the (yes, yes, this is a plus/minus!) the distinctive Strat two pickup position quack. Add more gain, and the the bright snarl of the bridge pickup helps it cut through a mix or band stage, and the two pickup position is somewhat humbucker-like. The Strat comfort curves are not a big thing to me, I'm convex enough they don't actually fit, and the Tele is not like playing a jumbo-sized archtop or something in regards to wanting for a forearm contour. I often play seated and the Tele is comfy for hours when I do that.

Now of course every one of those things is addressed and changed with many a setup trick, mod, or special models. I play a classic design Strat (albeit a reverse Strat with the bridge pickup going the other way) with pleasure. I have a trio of three pickup Teles, two with neck humbuckers. I have a dual humbucker Strat. I've decked and blocked trems and used a Tremsetter on Strats. I play a Bigsby Tele. Variety is fun. No reason to choose "or" over "and."