I think Yellowstone is best in August, when the bugs back off (black flies and mosquitoes). Same for Glacier Park. July is a nice time in GNP, with more wildflowers, but pretty buggy. The far north of YNP is nasty with pesky bugs in July, but higher up on the central plateau (the Old Faithful area) has less bugs overall, I've found.
As for comparing hiking out west to the East Coast area, you'll certainly get slammed by the elevation you'll encounter in Colorado and the Wind River range. You'll be hiking at 10,000-12,000 feet, which can be a bit tough for the first 2 weeks until your body adjusts. YNP hikes range between 5,000-8,000 feet, and GNP 4,000-7,000, so those areas will be a bit easier on you. The canyons of Utah are at a lower elevation also, but the heat of summer makes hiking harder.
I think it's best to do YNP, GNP, and the Winds in August, if not even into September after the crowds go home. Keep in mind that all three of those areas can treat you to an early snow dump after Labor Day, but not usually.
I also agree with the others that the best approach to check out the West is to do an epic road trip, see the sites, and wedge in a few 2-3 night backpack trips where you can (permits for GNP will be tough, YNP not so much). There are scads of cool things to see on your way out–the Black Hills, Devil's Tower, and even the Missouri Breaks. If you bring your passport, I think the finest scenic drive in North America is to go north from Glacier, take the alternate route to Banff via the Kananaskis highway, then over to Lake Louise to connect with the great road to Jasper. It's pretty much an up and back trip, but man, what splendid scenery.
Edit–Sorry, I forgot that you are flying, so ignore my comment about seeing places on your way out. But do consider that Banff-Jasper drive if you have a rental car.