What is the difference between the two Gore-Tex technologies in real world usage?
Specific factors:
FYI: I am planning on getting a jacket that would be for occasional mountaineering and regular commuting on a bicycle.
Which one packs down smaller?
Gore tex active shell, it consists of 2 layers instead of three and the outer is bonded ot the middle layer reducing it's bulk.
Which one is more breathable?
Again, active shell. The thinner fabrics will naturally allow more moisture out, there are less barriers between the inner and outside. How much more breathable is questionable though?
Which one is likely to last longer?
Gore tex Pro Shell. There are more protective layers, especially on the inside as active shell has no inner layer, and the layers are built of sturdier material.
Outdoorgearlab has some quite nice compilation of different shell materials with their history and use cases.
If you boil it down with respect to your questions then Active Shell is lighter and smaller and is significantly more breathable but at the cost of durability. As the guys from Outdoorgearlab write it, Active Shell
is not intended to be worn under a 70 lb. pack.
I haven't used neither one of both membranes but from the descriptions of the use cases I would guess that you might be fine with an Active Shell as long as you want to use it for cycling and some occasional mountaineering day trips where you use it primarily as outer layer in good weather conditions. Concerning that you say you want to use the jacket for regular commuting maybe the robustness of the Active Shell could be the limiting factor as it might wear faster–especially when carrying a backpack or the like while commuting.
