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The on-chip ones are semiconductor sensors and measure via the well known change in diode characteristic with temperature. The trouble with this is an odd millivolt or so of offset in the measuring throws the accuracy out. So it measures more or less the right thing but without great accuracy. You may well be of the opinion that that is not the greatest idea.
The thermistor ones are inherently accurate to +/- a degree or so, which you may or may not think is good enough. The trouble is that these are mounted somewhere other than on the chip and are therefore measuring the wrong thing (the temperature at some distance from the silicon) with reasonable accuracy.
Any of these is probably good enough to initiate a shutdown when something goes badly wrong, but if you have some other requirement, they may not be good enough, depending. Me? On initial prove-out I use an optical pyrometer, which isn't absolutely accurate either, but at least I know what it is claiming to measure and I have one hanging around! And if I know, +/- a degree or so, what the 'real' temperature is, I can use that to correct the limits that I set on the measured sensor temperatures (if that make a big enough difference to worry about).