Hi Simon, should be the same thing in theory. I suspect the output offset voltage of the op-amp is just enough to keep the gate triggered in one direction. What supply voltage are you using? It says 12V on the diagram but also 24V/28V DC next to where it says 12V. Don't power the gate from more than 15-18V whatever you do...
I'd measure the output of the op-amp with a voltmeter while adjusting the preset pot, and do the same while heating the thermistor with your fingers or a soldering iron. Remember that circuit is configured as an amplifier, not a comparator, and is a complete lash-up. You're relying on the triggering threshold of the logic gate for the 'comparator' bit which is extremely variable. (Well, not extremely as such, but extreme enough). You need to see what the op-amp output voltage is doing when you adjust the op-amp's inputs.
I really really wouldn't recommend using that circuit, it is far from satisfactory. The offset voltage and schmitt trigger threshold will vary with temperature and if you have a marginal design on the bench it will almost certainly fail in the real world. The microcontroller idea is much better, I've replaced plenty of comparators with microcontrollers in commercial designs in the past.