Suggestion #1:
Connect the two laptops together and try Migration Assistant.
What happens?
If this doesn't work,
Suggestion #2:
Use either CarbonCopyCloner or SuperDuper to create a bootable cloned backup of the MBAir drive onto an external drive.
(Note: CCC is free to download and use for 30 days, and SuperDuper will let you create a cloned backup without registering)
Take the cloned backup to the MBPro, and again try Migration Assistant.
Any better?
If this doesn't work,
Suggestion #3:
You will probably have to consider doing a "manual migration".
You may have to "manually re-install" your applications.
For items in your home folder, you can move them manually, BUT... you have to be careful about how you do it.
Clarification:
You CANNOT simply copy your home folder to the new location. I believe the home folder (and the sub folders inside it) are "symbolic links", which cannot be "simply copied" by the finder.
HOWEVER - you CAN copy all the items WITHIN the sub folders in your home folder.
Example:
You can't copy the "Pictures" folder.
But you can open the Pictures folder, select whatever you want, and copy those items to the -new- Pictures folder on the MBAir.
Same for the other folders.
For other folders outside the home folder that are not "system related", you can just finder-copy those wherever you want.
For a manual migration, you'll probably want pencil and paper so you can keep notes as you move along...