They're two totally different branches of the same tree. The world's top compound archer (Reo Wilde) cannot shoot recurve well, and vice versa. You might be using the same muscles, but it's a different shot process altogether. This does not mean you're not an exemption to the rule, but generally competitive archers stick to one school or the other.
I shoot compound for competitions, and do maybe 95% of my shooting with compounds. Occasionally I'll break out the recurve just "for funsies" but mainly the recurve is for loaning to my friends who are interested in trying out archery.
Just food for thought, if accuracy is your thing, then you'll want to go into compounds. I came into archery from a firearms competition background (USPSA, IDPA, 3 Gun, High Power). The first bow I picked up was a recurve just for it's simplicity. I spent about 3 weeks working with it and it just wasn't cutting it in the accuracy department. I want to be in the 10-ring, not just happy that I'm on paper. It takes a long time and a lot of training (coaching) to be good with a recurve. Time that I don't have and honestly time I'd rather spend hitting the 10-ring.
I bought a compound and was hitting Xs that same afternoon. It has a sight just like a rifle, need to adjust your group, crank your sight over. Takes all the voodoo out of archery and turns it into something this infantryman can understand, ballistics. Within a week I attended my first 3D competition, my group of 4 was me with my compound and 3 long-time recurve shooters (between the 3 of them they probably had at least years of archery experience). Despite shooting my targets from 5-10 yards further back, I managed to beat two of them on points. Technology trumps experience, I was sold on compounds for life.
If you want an idea of the disparity of accuracy between compounds/recurves/longbows/primitives. Just take a look at the
scores on 2nd leg of the ongoing Bowhunters Unlimited 3D League (I'm currently ranked 3rd in the CR category).
With that said, there is some appeal with stickbows. When you're not so concerned with hitting an X instead of a 9, stickbows can be fun for it's sheer simplicity. Easy to shoot, high rate-of-fire, easy to pull arrows out of bales, increased delight at actually hitting your target.