This is only my opinion. I'm not a soldier and I don't generally work with the infantry so take it as it's intended.
If you want to be a soldier, then join the Army. The Parachute Regiment is undoubtedly the place to go if you want to be a high-level (no pun intended) infanteer but is a lot harder to join than the RAF Regt and the infantry. The RAF Regiment is still a good job to have but, as Clip said, they have a very different wartime role to the Army infantry units.
The RAF Regt defend the areas surrounding airfields. I don't mean they walk round the perimeter fence: It means they go around the local area either directly preventing people from attacking the airfield/ aircraft when they take off and land by destroying hostile threats, or passively prevent attacks by patrolling, engaging with the local populace and scoping out likely areas of attack. The key here is that they are tied to the Airfield. As a general rule they won't go and conduct any sort of independent ops (unless they're a protection team on the back of an Aircraft that is landing somewhere dodgy). The other role where the majority of people are exposed to the RAF Regt is in the training role. The RAF Regt trains the rest of the RAF in military skills at both basic training and on your yearly refresher courses.
I apologise if this seem rambly, It's late and I'm knackered but I'll tidy it up at some point!