From personal experience, these are the relative advantages / disadvantages I have discovered personally or witnessed first hand:
Ole' Blue: - The lovable, closed-cell foam pad.
- Virtually indestructible (works even with a 6 inch gaping gash through it)
- Can be cut to fit (some people go for the shoulders-only approach)
- Bulky (full length does not roll up very small)
'Spensive Air Mattress - Such as Thermarest et. al.
- Soft (some people find them more comfortable)
- Thick distance between you and the ground (1/2 inch or more of insulating "dead air" depending on the model)
- Easy to puncture (requires care when packing / carrying a repair kit)
- Relatively useless when deflated (less-than advertised insulating power, though some models do have a thin layer of close-cell foam inside)
- Higher end ultra-light pads pack down pretty dang small
As for insulating power, since dead air is what provides that insulation. Even the highest rated (base on R value) high-end inflatable is going to be useless if it deflates. Closed-cell foam (such as ole' blue) are full of little isolated air pockets that trap air permanently and never deflate (though they can compress over time).
FWIW - I use a more expensive inflatable 90% of the time, largely for its small pack size, and better comfort (when it holds air through the night, which is about 75% of the time.) However, when I'm heading out on a snow-camping trip, I always bring the dependable insulating power of 'ole blue as well and double-pad it.