The Epi Les Pauls with the glued on necks are generally pretty decent for the money (avoid the ones with the bolt on necks). Build quality is consistently good, or at least I have never played one that I thought was poorly built. The stock tuners are a bit prone to sliding out of tune but otherwise I like them. The Mexi Fenders are also generally good and the tuners are fine but overall build quality is variable in my experience, most of the time they play no worse than 90% of the US models but sometimes you get one that seems to have been assembled on a Friday afternoon after a trip down the pub. As far as your present guitar is concerned, the Squiers themselves have been very variable over the 20-odd years they have been in production, for example the Japanese ones (early 80s) are essentially indistinguishable from US Fenders and play really well whereas the Chinese ones (early to mid 90s) are generally pretty awful... Indonesian and Korean models are somewhere inbetween. If you have a great Squier you might not notice much of a difference. As far as versatility is concerned I don't see how you could really go wrong with either.
If you are still considering options I would suggest a Japanese 1980s Tokai Strat, these guitars are the reason that Fender introduced their Squier line and IMO are absolutely fantastic... they are considered collectable these days so the price is probably about the same as a new Mexi Fender. ebay is probably the only place where you'll find them though.
Good luck, let us know how you get on.