I own next door, but can give you my general perspective:
1) Talikster has cash and they spend it the right way. They know what locals and tourists want, and they will do whatever it takes to give them the best "skiing experience." That means they will get more skier days and you will get some rental income. The advertising campaign for The Canyons last year was outstanding. The management of all the properties is generally excellent.
2) The more the Grand Summit books conventions the more rental income you are likely to get, particularly off season. Bookings have gone down with the economy but are improving.
3) Real estate is a crap shoot IMO regardless of what the realtors may think. It seems things have bottomed, but who knows? When the economy improves rates will start to rise. What will a 200bp rise in rates do to real estate prices when the cost of a mortgage increases by 25% or more? So long as you use the unit a few weeks per year the time it takes for RE and the economy to rebound becomes less significant.
4) The Park City area is a resort destination, not a place to visit for 6 hours a day. Die hard skiers may drool over Alta and Snowbird for good reasons, but the fact remains that most skiers on vacation also want a town with shopping, restaurants, museums, etc. I think the key to additional skier days (and your rental income) is not competition with the other two local areas. The real issues are the national economy and competition with the Colorado ski resorts.
Good luck with your purchase!