I would expect that it's a mix, although you couldn't put a 10,000 hour airline guy into an F-15 and expect him to perform what was needed most likely any quicker than a new guy (thinking about what Bunk, Hacker and AMG have said about flying being one aspect that is secondary to being a weapons operator). I don't think even that UPS Airbus guy, with his hours and hefty paycheck could spend a day working an AT-802 like T-cart does in the rice fields (although T-cart probably has more total time - either way, you get the drift). So, the kind of flying you're doing, mixed with training, mixed with experience in some recipe creates the stew. Ask yourself, Boris at 7,000 or Bumblebee at 4,000 or Kellwolf at 5,000 - could you fly a P-51 or F4U as successfully as the sub-300 hour WW2 guys? How long would it take you from your starting point now (with your hours) to become accomplished at flying the Mustang or Corsair, using it as a weapon effectively and not balling them up on a go-around or a landing? I think it would be less than the 250 or so hours that the WW2 guys had, but how much less?
When a pilot fly's a certain aircraft, flying specific profile's, missions, etc, they do become very good at what they do. However, they may not be very good at other aspects of flying but can probably pick it up quickly given the chance. For example, the pilots that fly BFM down here in Kingsville do it day in and day out. Matter of fact, 95% of what they fly is BFM. Then they go do a NATOPS check and suck at certain things, like PA's, aero, etc. Given a few flights, I'm sure they could master it. What I do 90% of the time is formation flying, most of it as a lead in section and division. I went out and did a NATOPS flight not so long ago and for example, performing the the squirrel cage, I was just awful. Again, this is a small part of flying but it shows how an experienced pilot can be less than par depending.
Now take that same experienced Goshawk pilot and put him in a C172, Seminole, whatever, it may take some time to develop the flying skills to master that aircraft. However, being used to inverted flight, aggressive flying, formation flying, maybe having an engine flame out a time or two, brings confidence and experience to the equation. Due to that experience, the pilot's decision making, adaptability, SA, etc are all enhanced...more so than an inexperienced pilot.
I have 3000 hours, in both jet and multi-engine prop, I've lost a motor at 100'AGL, had a pitch locked prop, a motor not relight, had to shut down a few, have over 500 carrier landings (left and right seat) so it has enhanced my experience but put me into an RG Cessna and expect me to fly it well, like the CFI who has been instructing for hundreds of hours, it's going to take me some time. I wish I were that good but I'm not. But I have the confidence that given time, I will be good with that aircraft due to my experience and background.
The most difficult flying I've had to do was coming back to the 45 as I had not flown a jet in 14 years and had been out of the cockpit for over 18 months. The syllabus is the same for all IP's in the T-45A/C, you get 20 flights, about 33 hours. You do it or don't and for most of it, I felt like I was hanging on the slats. My point here is it's tough for more most pilots to go from one platform to another, at least if you're average like me. I always ask my students, you know why most of us are average? Cause there are days we are plumbers and days when are Blues. Things that help us are experience, confidence, quality and quantity of training.
I think this topic came up not that long ago.
I credit the fact that I don't any "stories" because of this. 
