For me, it would be the Strat, hands down. I don't care for the Les Paul neck, and I've never played an Epi that I liked. On the other hand, I've got a Squier HM model that I've worn down the frets on and still play regularly despite having a couple of much more expensive guitars. In fact, I'm considering having the frets replaced on it, even though it's a fairly cheap guitar, so that I can continue to play it. You, on the other hand, might love the Epi and hate the Strat.

Choosing a guitar is very subjective. I'd say, based solely on my experience and that of people that I know, that they're probably similar in quality, bearing in mind of course that good guitars and lemons are both found in every brand and price range. It's hard to give advice on which guitar to choose in a forum like this. Folks can share their experiences with each one, but ultimately, it comes down to putting them both in your hands and seeing which one feels better and works better for you.