It all depends on what model Strat your talking about. As for me, I've always played guitars with fairly thick necks. 50's Classic Tele's, Wolfgangs, and the big daddy '74 Les Paul Standard, which has the huge neck Gibson was putting on the Deluxe models back in those days. I never had a single problem with my hand UNTIL I bought a Les Paul Classic with that thin 60's style neck. Within 3 weeks of owning that guitar, I was seriously worried about my playing future. My hand cramped when playing and was numb/tingly for hours after playing. I kept thinking I'd finally get used to it but the problems got worse very quickly. Finally, I put all of my guitars for about 2 weeks. Started back up with my old guitars and didn't experience too much discomfort. Got the LP Classic out and was right back to not being able to play. I sold that guitar 6 weeks after buying it. It took about 9 months to a year before my hand stopped bothering me. I now will only play a guitar with a thick neck and big frets. Dunlop 6100's are my friends. To me, thin necks make for great firewood.
That's my story and I'm sticking to it.
)
I'd take one 
