Here's the thing about temperatures, I almost never adjust the temp, I stay at 700F almost all the time. There has only been a couple of times where I needed extra heat because of what I was soldering. I think that the induction heating on demand will cover the rare times I need more. Actually, the price of the tips are very compatible, almost the same. As far as other brands, I haven't thought much on that and as far as used, it will depend on the unit. Almost all of my test gear is used, but I am leaning towards new for the soldering Iron. I don't want a used higher end unit that was in a production environment and may not have been taken care of as it should have been. What other brands/models did you have in mind. I try to keep an open mind and weigh options.
I don't switch temperatures all that often either, but it's nice to have in the instances you need it. And without any additional cost.
Particularly useful if you find yourself working with something that's thermally sensitive enough you need to use Sn42/Bi57/Ag1 low melt point solder (138C/281F), as a temp controlled station will allow you to work at lower temperatures than is possible on RF heated Curie point stations.
Also understand, that the extra capacity/power poured into a joint capability associated with induction units, isn't exclusive to them at all. There are temperature controlled stations that can pump in the heat just as well or even faster (depends on the designs/stations being compared). For example, I'd stack a JBC against a Metcal or Thermaltronics running at 13.56Mhz. Weller makes some fast responding stations as well, and the Hakko FX-951 you're looking at is no slouch either (any of these will blow the doors off of your 936).
Demos on youtube are available ^. Generally speaking, you'd want to take them out for a test drive (typically a 30 day trial), and see for yourself.
Given the sources you're looking at however, I'll presume this isn't possible.
I get wanting new, but there's a gap between the $100 and $300 mark (not much there, save the FX-951). To get absolute top end performance, you'll need to look at ~$350 mark -minimum- if you insist on new. You can approximately half that number buying used if you're patient. If you do look at used, examine the photos closely. If it looks like it's been to hell and back, skip it. Which puts you within your budget, and gives you options beyond the two stations you're currently looking at (more gasoline on the fire
).