I have done 2o/2o for years (btw - no shoulder injuries..taught correctly, it is pretty safe). Here's what I tell my students.
Running contact have the pros of being fast, furious and POSSIBLY a tad bit safer. I say possibly because the number of reps you have to have to teach a TRUE running contact is ENORMOUS. A TRUE running contact is harder on the dog than a 2o/2o.
When I say a "TRUE" running contact, I mean the type you are looking to do. A method that has TRUE criteria the dog can understand. Not just, "Slow down and hit the yellow." The dog has no clue what that means, and you wind up with a "managed" running contact, meaning you HAVE to physically be at the contact to slow the dog or even point the dog into the yellow. A true running contact has criteria the dog can understand. For instance, the dog can learn "2 hits, shorten the stride for the last hit" taking the dog into the yellow with that criteria. Trykman's method teaches a TRUE running contact. Almost ALL running contacts in the US are managed running contacts. Almost ALL 2o/2o contacts in the US are managed 2o/2os too.

You know you have criteria if your dog hits the contact 99.8 percent of the time without you needing to be present. (ie. will your dog hit the contact with you 30 feet away laterally, to the front or to the back). Another pro to running contacts is that if you wish to be on the World Team or compete Internationally, the RC can really help. You CAN do these things and WIN with a well trained quick release 2o/2o, but the RC does give a slight edge internationally. If you aren't going to compete internationally or be competitive at Nationals, then this may not be your bag.
The cons to running contacts are less reliability (you can get a 100 percent 2o/2o contact, but will always have a few fly offs with even a great running contact), no static contact at the end to help you get to position for the next section of the course, to have a TRUE running contact you have to own the equipment to train daily (with a 2o/2o, I train on a low board and do very few reps on equipment making it easier on the dog's body), you have to be prepared to train for 100s of hours, it is FAST.
When I have a new team come to me, I examine the team as a whole. Is the handler fast? Is the dog fast? Is the dog small? Is the dog drivey? Is the dog slow? Is the handler young? Is the handler REALLY motivated to train? Does the handler have experience in agility? Does the handler have experience in training (ie high level titles in obedience or other sport)? What is the dog's structure?
When a team has an experienced handler with agility experience who is also young and very athletic with a fast dog with loads of drive, I will give them the option of a running contact, explaining the pros and cons. If the team has World Team aspirations, we really look into the RC as the best option. If the dog has structure issues, we look into a true RC - but generally we look into a managed RC with the understanding that the handler MUST be present at the bottom to help the dog find the yellow with some physical cue (usually a combo of forward motion, hand signals and voice) and the understanding that it will be less reliable. We do a "managed" contact because it requires the least amount of reps on the equipment, helping keep injury at bay for these dogs with structure issues. I do not recommend 2o/2o or other static contacts for dogs with structure issues. I also have recommended running contacts for slow dogs or smaller dogs who are very likely to naturally stride into the yellow.
I recommend the 2o/2o or other static contact to teams with one or more of the following: an inexperienced handler, a slow handler, a handler with troubles understanding training methods (ie. clickers, etc.), handlers who don't own the equipment, dogs who have sound structure, dogs who are highly drivey ad thus likely to blow a contact, etc. Most of my new students start with a 2o/2o.
Think hard (as you are) about which poison you will be training. Then, train it. Stick to it. Most people give up on running contacts because a TRUE running contact is so hard to train. This is bad because then the dog really has NO CLUE what so ever what to do at the end contacts. Retraining is NEVER has solid as training correctly from the start.
For me, I always choose a 2o/2o contact. I am a physically limited handler who runs fast dogs (over 6 yps in JWW). The 2o/2o works well for my teams because it allows me to get into position to easily handle other sections of the course.
One more con to running contacts. Because they take SO LONG to train properly, I see a lot of teams get running contacts, but they have ignored all the other aspects of agility training in their search for the RC. These teams are woefully behind, and it is frustrating to watch the dogs confidence fail as they don't understand handling. They do understand contacts, but contacts are only a tiny bit of the sport.
So, are you healthy? Are you young? Have you trained to titles in other sports? Are you truly read for the cons of a running contact? Do you have international or national aspirations? If so, go for it. If not, then stick to the tried and true 2o/2o. (Which, btw, is actually very seldom trained well either, but does work better as a "managed" contact than a "managed" running contact.)
Here is my boy doing some 2o/2o with a static hold or a quick release. You can see we waste a few seconds doing this, BUT I get into position for the Q. Instead of 1st in Standard, we may get 3rd because of this, BUT we get our blue ribbons in JWW.
https://www.youtube.com/watch?v=sDAJ789tdts