In 1997 I got a job at a local PCB factory; prior to that, I'd never soldered before. They had Metcal STSS and MX-500 solder stations there, so that's what I learned to solder on.
By the way, the STSS and MX-500 are the same thing for all intents and purposes; same handpiece, same line of tip cartridges (STTC-xxx), same wattage; the latter is just a newer version of the former with a couple of trivial added features and a cosmetic redesign of the power supply unit.
At first I didn't realize there was anything special about a Metcal, because I had no experience with anything else. At some point, one of my co-workers mentioned that he looked up the Metcal MX-500 on the internet and said it cost about $500, which was my first clue that it was something out of the ordinary.
One night I asked my supervisor if I could borrow a soldering iron for the night, because I wanted to do some soldering on a full-range speaker box I was putting together. He said, "Sure," and reached under his desk and pulled out a vintage Weller soldering station. I wasn't impressed with that thing at all. For starters, it took a while for the tip to reach operating temperature (over a minute I would say), instead of several seconds like the Metcal, and the ergonomics were horrible. The grip was huge, over an inch in diameter I'm guessing, and the grip-to-tip distance was something like 5 or 6 inches. To illustrate the loss of control you get with such an unwieldy instrument, wrap a pencil with tape until it is over an inch in diameter, then grip it 6 inches from the tip, and try to sign your name as neatly as possible like that.
After I stopped working at the PCB factory in 1999, I needed a soldering iron for various projects at home, so I bought one at Radio Shack for $7. It had about the same poor ergonomics as that Weller, but it took even longer to heat up (5 minutes or so) and the tip was junk; it corroded in no time. I could make good quality solder joints with it, just as I could with a screw driver heated with a propane torch, but I hated it.
In 2007 I made up my mind to get my own Metcal, because I'd started acquiring 1980s arcade machines and found myself needing to do a lot of work to their PCBs and monitors. I managed to get a hell of a deal on a working Metcal STSS (complete with handpiece, one tip cartridge, and workstand); just under $40 shipped. The tip cartridge that came with it (STTC-125) worked fine, but I ordered a new STTC-126 tip cartridge for it, because I had a strong preference for that particular style of tip at work; I used it for most everything. ~10 years later, my Metcal still works perfectly, and so does that STTC-126 tip cartridge that I bought at the same time.
In any case, as others have mentioned, the differences are: ergonomics, heat-up time, and ease/speed of changing tips. The Weller you have looks to be a lot more ergonomic than the ancient Weller station that I borrowed from work that time, but it is still a far cry from Metcal, JBC, and other high-end solder stations. A high-end soldering station won't necessarily improve the quality of your solder joints, but it will be more versatile and it will make soldering more enjoyable.