I have a couple of cheap knock off stations from Amazon. Both of them use a huge transformer instead of digital. I heard a guy on Youtube tearing a couple of the cheap stations down and said he preferred the nice, large heavy transformers to the digital type. He said there is just less going on in the transformer type, and he liked that. He didn't elaborate.
So, what's the difference?
Just to reiterate, digital vs analog has nothing to do with the power supply type. Most digital soldering stations use transformers. And though I haven't seen one, it'd certainly be possible to build an analog soldering station using an SMPS.
SPMSs are rare in soldering stations, perhaps because of the leakage voltage on the outputs if the device isn't grounded properly. (The EMI reduction class-Y caps overlay about 1/2 the mains voltage onto the DC outputs, if not grounded.) This could easily kill a component. Sure, if a manufacturer provides a proper grounded SMPS, you'll be fine most of the time, but what about when someone has a bad ground in their receptacle and doesn't know it? A transformer-based unit is less likely to cause problems in that situation.
Finally, I do believe that transformer-based supplies are more reliable. I'm not saying that SMPSs are inherently
unreliable, just that a transformer is
more reliable, all else held equal. (Obviously, all bets are off either way if something is made badly.)
We just got some Weller WSM 1 stations at work, and they use a simple ungrounded external power brick, seemingly relying on a separate potential equalization jack for true grounding. Not sure how I feel about that...