The difference is in your priorities. Which one is more important to you?
- Thin size and light weight
- Overall versatility and more storage space for the price
If you need #1, you get an Air. If you need #2, you get the Pro.
SSD/flash storage is much faster than the old hard drives, but it's also much more expensive per gigabyte. People choose SSD because speed is more important to them than cost or capacity. But it sounds like you might prefer storage capacity.
Check the capacities listed for the Air. If those are too small, or if you think it's too expensive to upgrade to the SSD capacity you need for your music and videos, then you should get a MacBook Pro with a standard hard drive instead.