Zale,
Ultimately, it'd be best for you to have a good hank of 9/16" AND a hank of 5/8" stable braid. It's definitely nice to have something lighter in weight when you don't need the big stuff. But if I could have JUST ONE, like you originally asked, I'd still go 5/8".
If all you have is the 9/16", there will be times when you wish you had bigger. And yes, maybe...just maybe...you're trying to cut too big a piece if that's the case, but peace of mind is a good thing in this biz. Plus there'd be less cycles to failure for 9/16", if that's all you had. IMHO