Pros
They treat you very well over at Swissport, and they arrange you very well with the airline. Usually are pretty willing to help and have a decent employee support mesh. You get to go to whichever airline they are being hired by as long as you meet the airline's criteria and they interview you to know you're what they want to hire. You might get into an actual direct contract with the airline if you take this opportunity and then start looking out for the next step.
Cons
Many... They will pay you less than working directly with the Airlines would give you, switching airlines won't mean better salary in some scenarios, even if you switch to a better airline (if you're going from a good airline to a not so good one this is a "Pro" I guess...), you don't get airline benefits, if you're a bit far from the airport you're going to have trouble with the salary and keeping up with travel cost. You're not working directly with the airline, so there's chance for many troubles to happen when you're at the airline that they can't get a hand on and you can't do much with it either.