What are the benefits of using the doors for a jump in a C-130 over the ramp?

There are actually few reasons. I have jumped both ramp and doors. I did a Mass Tac last week. The only time you see a Ramp Blast is with small units such as a SF or LRS Team. When you are going with Mass Tacs you can get more out by using both doors. If you only have 10 seconds of green light you should be able to use both doors and put more than just using the ramp. I have never seen anyone use a Ramp for a Mass Tac. To me it would seem far to dangerous. The location of the JM and the Safety would be an issue. Plus could you imagine if a guy fell down on the ramp. It would create havoc. He has no where to go. While jumping doors you could just pull them to the side and let the rest jump. In addition to all of this I imagine that it would also create a lot more hazards too. Just a bit of turbulance you could lose the cargo handlers in the back.

Higher rate of exit and MORE jumpers.. over the ramp is limited to 40, jump doors you get 64 in peacetime, 76 in combat. Thats is why you see the jump doors used in standard procedure.
Chasing heavy drops (our gun truck) and smaller size element (4 man crew per truck) we would jump ramp.
My small Infantry platoon in Alaska was the only one allowed to request and make ramp jumps the three years I was at Fort Richardson. When I was at Bragg, the only ramp jump I did was proficiency stuff jumping static line with special people (SF mostly) They would need 10 static line jumpers as part of the package that wold take them up to alt for free fall. ... So static line jumpers were many times found from the regular airborne community

Because if Special Forces didn't do things in a special way, they'd just be 'forces'?

Sorry...couldn't resist.

Good question. I'm pretty sure the main benefit is the amount of Paratroopers exiting the door. See attached illustration. Tail gate jump you can only use 2 anchor line cables (20 pax each / 40 total) versus 4 (64+ pax) on the door exits. So you can do a mass tact from the doors, but not the ramp. Well at least not an official mass tact. For more info refer to TC 3-21.220. Anyways, I'm not pretending to be a jump guru as I just researched some of this interesting info. I also recommend this this cool and interesting link: http://www.combatreform.org/llparachute.htm

It's been many moons, but I think doors maximize safety and getting max troops out -- I've never jumped more than one anchor line cable off a ramp (3rd SFG) and we took the whole ramp to avoid the d-bags. With doors (82nd), all cables are in play and d-bags are not as big an issue.

If you use the ramp, no slamming on the side of the plane if you get hung up.

Ramp exits encourage walking out of the aircraft vs jumping up and out. When you simply walk out and fall there is less chance of malfunction due to jumper error. Ramps also lead to people being more aware of their surroundings as many door jumps are night jumps regardless of the time of day because troops have their eyes closed.
I always preferred ramp exits from fixed wing and even rotary aircraft, the view is amazing and CH-47 jumps were my all time favorite. Them Night Stalkers will take you on a hell of a ride and then you just step out into the heavens.
Good topic LTC Yinon Weiss

None. Jumping out of a perfectly good airplane from any door is silly. :D

Of course it is easier to push those of us who feel that way out the ramp than the door.

USASFC jumps MC6 steerable chutes, so both paratroop doors can't be utilized at the same time. You're choices are jump one door, jump one door and then the other, or ramp. Ramp doesn't require a JM controlling static lines and doesn't require a strong exit. Basically like a Chinook jump.

The only thing I can think of is that putting a large amount of jumpers out quickly is easier to control the output timing using the doors to prevent collision. Jumping a tailgate high performance has honestly never been my favorite thing anyway. Tailgates are great jumps from chinook or casa though.