I've, quite stupidly, had a Squire Strat for 7 years now. I fancied a new guitar so had a try of one in the shop, I couldn't believe how much I enjoyed it, particularly the ease and effortlessness of playing other guitars.

I like rock, hard rock, a little metal, soloing, shredding (I currently can't but I'd like to be able to). I also like playing clean such as Stairway to heaven intro and Hotel California intro.

The guy at the shop recommended either the Jackson JS32 or the Schecter Demon. I tried them both and I had more fun with the Jackson, played it easier and quicker. But I like the Schecter as the quality is better, and better pickups, though the neck is wider (a con I felt).

Are there others I should consider? I tried 4 guitars (another Jackson with FR and an LTD - perhaps Metallica's lead guitarist signature) in total, but I'm not any closer to deciding, I enjoyed them all.
I would go with the Jackson if you enjoyed it more. The way I look at it the more you enjoy it the better you will play with it.
Gibson Les Paul Classic
Fender Stratocaster (Mexican)
Hagstrom Ultra Swede
Music Man Axis Sport
I have a Jackson JS35 (which is probably pretty much the same as a JS32) and I really like it.

But, since you buy it for yourself, you are the one who has to decide.