I think what has been affirmed in this thread is that the name on the headstock means little and whatever works, sounds and feels comfortable to you is the winner.

I have a Strat currently and have own an LP (and am soon-ish to own another) so they are good guitar for me and loved them both for different reasons. I somewhat have the fortune of being able to own more than one guitar these days. Back in the day, I had to find one guitar that served as many masters as I could. So I had to choose (...it was the 80's and I chose a Kramer American Baretta). I like that I might have a little smargasboard to choose from and thus why I could never actually answer the original question.

If you have to go with only one axe, forget the name on the headstock. Just play it and if it sings and fits like a glove, there's your choice.