Mainly I would say get a guitar in between having rubbish stagg-style cheap junk and a reasonably pricey one. That's not always the best option, but don't invest heavily unless you are certain.
Try as many guitars as you can. Go to guitar shops. Don't just look for ones that are popular or famous - my favourite guitar is my Fender Flame which they made for 1 year in 1984 which I found second hand in a guitar shop for less than £600. It doesn't have to be Strat/Tele/SG/Les Paul to be good.
When you're trying them in guitar shops, try them with your amp (if they don't have one like yours, then once you've narrowed it down and are reasonably confident, see if you can bring your own in). I assume that your amp is also OK - there's no point spending a grand on a guitar with beautiful pristine tone if you're going to run it through a 10W practise amp or some horrible solid state modelling piece of
*any expletive of your choice really. as long as it's a noun. a verb would be thoroughly inappropriate in this context*
If there's anything you don't like about the guitar, just don't get it. It's not something you need to compromise on - there are so many guitars in different styles, why get something which doesn't really work for you?
Also, unless you're gigging in these sorts of bands, I'd advise to get something versatile, so that if you feel like playing something more complicated you'll be able to - don't pick something where power chords and open chords are about all you can get your hands round, for example.
Mostly though just keep trying as many different guitars as possible.
There is a reason these guitars you mention are so ridiculously popular, but I personally would prefer to venture off the beaten track a little and go for a guitar which would set me apart a little more.
On the other hand, if you were just asking for advice on the choice between the 2, I guess I wouldn't be much help.
How long have you been playing for?
Also the action is adjustable by fiddling with your bridge height, and you are hopefully aware that it is actually possible to change your strings if they're too heavy...
Before investing in this, sit back and think honestly to yourself about whether you are good enough to warrant this - no offence meant but at a certain level more expensive equipment won't really make you sound much better, and you're better off sticking with a rubbish one, then getting to a really good standard, THEN upgrading once you're really familiar with your instrument. (Sorry if that bit sounded patronising - I don't know how good you are obviously or how long you've been playing for).
Either way all the best with your guitar-ing
Oh and I almost forgot - this is what my baby looks like:
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Isn't she hot