Your question is a bit open-ended, so I'll answer as best I can.

The web version caches the map image once you load up a map for the first time. So bandwidth is not affected in that regard and loading is minimal, as map tiles are loaded on-demand.
The added benefit of mobile is that the mobile version will not be using map backgrounds at all, so download bandwidth is taxed less. What will need to be downloaded is the map information (placements, shaders, etc.) these may or may not be cached depending on the cache conditions (so I cannot give you a definite answer for that)

So, loading will be faster, less download bandwidth is required. With all this being said, it's subject to change. I hope this answers your question