1. Village/Town Feel?
2. Ski School for Kids? My kids are very shy.
3. Amount of Easy Skiing Runs for Kids/Wife?
4. Non Skiing Activities?
5. Crowds in February (not President's Week)?
I just saw this, and found it interesting, as your situation is so similar to ours! I have 3 kids 8, 6, and 4. We've been to Park City twice and Sundance Ski Resort once. My son, 4, just skiied for the first time last year at PC. However, we are really considering Steamboat this year. We go the weekend before Pres. Day, so Feb. 8-12 this year. Online reviews are hit or miss, but the town sounds awesome, and the big one is a 5 hr. total trip from the east coast. I am interested in anything else you find out.
I went through a similar research process for our family trip this year... coming from east coast I was deciding the best family destination for more than just skiing (but mostly skiing). I narrowed my list to Snowmass, Telluride, and Park City. Fortunately, a Canadian friend of mine suggested I look into Whistler/Blackcomb and in the end that's where we booked largely because it ended up being less expensive for better accommodations than any of the CO/UT resorts (kids free at Whistler through March - free lift/rentals/transportation - even lessons if adult takes lessons). We just returned yesterday and I will tell you without reservation it was the best sk vacation I have ever had and considering it cost less than similarly appointed trips to the CO/UT destinations, I couldn't be happier. It had everything my family wanted including epic ski conditions all 5 days.
This entire forum is suffering from neglect. Let's be serious, if you want access to great skiing Park City wins hands down, you can ski Canyons, Deer Valley and Park City all, 5 min drive on a shuttle away, and all have their own characteristics, and I assure you Deer Valley is fun to ski, forget what young or old men afflicted with fading testosteronitis ! on the board say, it's a good place.
Steamboat is cool and all but is like a little hill when you combine PC, DV and the Canyons. And if you are adventurous , you could go ski the best mountain in Utah via shuttle/hired car Snowbasin, those lodges are to die for!
And if you get really adventurous take a ride to the Cottonwoods, Big or Small, Alta/Snowbird generally have the best snow in Utah, actually funnily true right this minute but often skiing Snowbasin so much better than the Cottonwoods.
Ok..am done best
1. Village/Town Feel? Both towns are great. Both have an "old" feel, at least down the main streets.
2. Ski School for Kids? My kids are very shy. All four resorts have great ski school for kids. These resorts know how to teach and make sure the little ones have fun.
3. Amount of Easy Skiing Runs for Kids/Wife? " Easy" meaning green or blue groomers? The Canyons has little in purely beginner runs. All three PC resorts have more intermediate runs than you can ski. Steamboat has enough intermediate runs, but like dustyfog wrote above you have a lot more options around PC. Deer Valley is ultra-groomed. Canyons and PCMR groom plenty so you can find smoother runs everywhere.
4. Non Skiing Activities? There is the usual tubing, hot air balloons, snowshoeing, x-country skiing, dog sledding, romantic dinners, sleigh rides, etc. everywhere (it seems). PC has a nice in-town museum and the Olympic Park/Alf Engen Museum is next to the Canyons. That is the largest ski museum (I believe) in the USA. The museums are great for kids. Steamboat Spring has a nice museum (Tread of Pioneers) the kids will like. Both towns have restaurants suitable for kids. The Heber Valley Railroad is close to PC, which the kids will love. Again, SLC is only 45 minutes away if you want to catch a basketball game or concert or whatever.
5. Crowds in February (not President's Week)? You are west of the Continental Divide. Don't worry about it.
You forgot to ask about the access to airports. PC is maybe a 45 minute drive on good roads from the airport. Easy. You will have a great time in either resort.