What's safer, Airborne or Air Assault?

Per capita? Air Assault is probably more dangerous than Airborne.
However, no one is ever going to fast rope a brigade on to a 3 square mile area in about 5 minutes flat along with equipment, guns, and vehicles, so it's kind of a difficult game to figure out.

I never felt that jumping was super dangerous, just a bit wierd the first few times you do it. I think I'd be more scared to fast rope.

Walking in as a leg is safer

you drop slow and become a target, if you are droped off by a bird you can take cover faster so I say air assault.

Anything that involves aircraft and the movement of supplies and men is inherently "dangerous". Accidents can happen at any time and conducting air assault operations (including parachuting) is risky business. However, doing a static-line parachute jump is far more dangerous than doing an air assault due to the high risk of personal injury jumping from a high performance aircraft traveling near 200 mph and hitting the ground hard.

The biggest threat to personnel performing an air assault is the aircraft itself if it suffers a major malfunction and crashes. Getting off the helo or rappelling from it is risky, but not nearly as dangerous than coming down in a parachute, not even close. I've actually suffered a small fracture in my neck during one of my jumps and numerous other injuries as a paratrooper, so I know firsthand how dangerous it is. Air Assault is a pretty straightforward mode of transportation and rappelling/fast-roping doesn't have the same risks as parachuting. Airborne operations is probably the most dangerous thing you can do in the military, especially when you do static-line jumping.

As far as inserting on a "hot" DZ/LZ, I would hope that other options are available, but helos are versatile enough to get out of there if the enemy has too much fire, but careful planning and intel are more important factors.

There have been more soldiers given assault landing credit for airborne operations than air assault operations. Your chances of fast roping anywhere besides a training environment in a conventional unit is far less than a conventional unit doing a combat jump. That said, your chances of being injured are just as high doing fast rope operations as they are in doing airborne operations. Your chances of being injured just flying around in a helicopter and landing on a LZ are laughably low unless you charge headfirst towards the rear rotor or do something equally stupid. The reality is, aircraft are too valuable to waste on inserting troops into a hot LZ.

As others have said, it depends...

There are too many factors that can determine whether one can go from safest, to most dangerous. However, I'd guess that in a perfect-world scenario, Air Assault has fewer things that could go wrong, therefore making it a bit safer method.

Doesn't matter they never will be used in a hostile environment unless they want to get shot down.

In LRS, we practiced both, plus zodiac insertions/exfil. Personally, I prefer just leaping (and I use that term loosely considering the weight of combat equipment) into darkness versus reaching for the rope. I've roped out of 60s and 53s, and one thing I never got a warm-and-fuzzy on was reaching out the side of a 60. 53s have a "hell hole," and it's a little comforting that a little shutter won't send you out into the inky night. And I'd prefer either of those to carrying a zodiac over land… no thanks.

Here's something you may or may not have seen from Canadian Special Forces demo video amount training repelling onto a rooftop. No real element of surprise. Still looks cool though.
https://youtu.be/8dWYlgl_6x4