Skipper hit the nail right on the head. To answer Ziggy's questions, yes the "indicated" stall speed would be identical, but the true airspeed at which the wing stalled would be higher. (The rule of thumb is approximately 2% per 1000 feet above SL.) This is the primary reason why for any given weight the landing rollout distances increase with altitude. As the airport elevation increases, the aircraft's "true groundspeed" at touchdown is greater and the greater the speed, the longer it takes to stop. As an example, take a SL airport on a standard day. If you touchdown at 60 KIAS, your GS will also be 60 KTS. Now, take that same 60 KIAS touchdown at Denver and your KTGS will be about 10% greater or roughly 66 knots - hence the longer landing roll out. If you had the power, the wing would still stall at 100 KIAS as FL300, but the true airspeed at that altitude would be around 160 knots!
As far as climb performance degradation goes, loss of power is the primary culprit as far as the aircraft we fly. Normally aspirated aircraft lose power with altitude. An aircraft's climb ability is directly proportional to the amount of "excess" power that it has available vs. what is needed to maintain level flight. For example, if a 200 HP normally aspirated airplane requires 100 HP to maintain level flight it would (at SL, ISA day) has 100 "excess" HP to use for climb. At 10,000' MSL, the engine might only be able to produce 130 HP, leaving it with a 30 HP surplus. This is the reason why turbocharged aircraft perform so well - you would be able to maintain SL power up until you reached the "critical altitude" for your particular installation. In some cases this is as high as 18,000' MSL.
This is also why light twins typically perform so poorly on one engine. Take, as an example, a Twin Comanche with two 160 HP engines. If that airplane required, say, 150 HP to maintain level flight it would have 170 "excess" HP to climb with. If it lost an engine, it would have lost 50% of its available power, but with just 10 "excess" HP, it may have lost 95% of its ability to climb. Light twins have two engines because they need two engines!
As far as turbine powered aircraft go, the same rules apply. Turbine-powered aircraft are, in essence, normally aspirated, in that they lose power with altitude also. Granted, aircraft designers can play a few games, such as "flat-rating" powerplants, but regardless, they still behave as if they were normally aspirated. Additionally, with turbine-powered aircraft you have to consider the effects of high-speed aerodynamics. Skipper recommended a great book - I highly recommend that you get it for your aviation library.