If you decide on Utah and can stay on the mountain I'd do Snowbird for 3-4 days and then maybe Snowbasin for 2 days (no lodging on the mountain, closest is probably ~20 minutes by car) or maybe the Canyons for 2 days. There's plenty of exploring to do at Snowbird. Also, if you don't mind splitting up for a day or two you could ski Alta while your buddy's at Snowbird. If you do Snowbird maybe you can convince your financier to spring for a day or 2 of heli with Wasatch Powderbird Guides. Another option for the 2nd half of your trip is Solitude and Brighton in Big Cottonwood Canyon. I'm not a big fan of Solitude but it'll definitely keep your interest for a couple of days. Brighton is supposed to be great for snowboarders. You can stay on mountain at Solitude. You can't do Deer Valley as they do not allow snowboarders.
I've never been to the Aspen area resorts, but there's plenty of terrain between Ajax, Highlands and Snowmass to keep you busy for the entire week. The bus system is supposed to be great. Snowmass is supposed to have tons of on mountain housing available. If someone was going to pay for a week of skiing and lodging for me, I'd probably choose Aspen b/c I've never been and since it's quite expensive I'm not likely to pay for it myself when I can find equally good, if not better terrain for much less in Utah.