I am looking at getting a multiple stage heat pump from Trane, and they have several options, specifically the XL19i and XL16i. Does anyone have experience with a dual stage heat pump? Also, what is the difference between a dual compressor and a staged single compressor?

While I can't specifically address the Trane heat pumps, I have a Trane 16i gas pack up on my roof (what a crappy location for an HVAC system!) which has the dual compressors on the A/C side of the unit. I can say that it works fine and at 5,100' elevation in northern Arizona, the larger compressor rairly comes on. Any compressor on your roof will be noisy. It sounds like you are in a drum in the room below! I'm sold on Trane and my next home will have a 19i as it will be at a lower elevation with more summer cooling loads. It will also be on the ground with a separate air handler in the home like God intended! The only advantage of having it on the roof is that it is harder for the 'druggies' to steal the copper.

if you live in a mild climate (not too hot not to cold),

a airsource heat pump like xl19i will probrably work great!