The advantage of 10w30 over 5w30 is that it uses less viscosity index improvers, so it's more shear stable, scores a higher HTHS number, a better Noack number and you'll typically burn less oil with 10w30 than 5w30, especially in the LS1. A lot of guys have come to me with advice on what to do about their oil burning LS1s, and when I tell them to switch from 5w30 to 10w30 they will often come back a few weeks later and tell me their consumption is greatly reduced or eliminated.
I also feel for extended drains that 10w30 is better than 5w30 as it will also keep the engine cleaner (due to it's lesser amounts of VII) So if you don't need 5w30 for your weather, go with 10w30. I'd only go with 5w30 in an LS1 if it were consistently below 0F. This recommendation is for any pushrod V8, I'd lean more towards going with 5w30 in an OHC engine.