With differences in tuner performance, that will not tend to be noticed when they all are decent and the signal from the station is good. Differences in tuner performance tend to show up in situations of a poor, weak signal from a radio station. (Or, for some aspects of tuner performance, an overly strong signal.) And then to properly compare, one would have to be using the same antenna, in precisely the same location, which most people are not going to do when comparing things. In most locations, the tuners in all three will be fine and be of little, if any, practical difference. It is only in situations where one is trying to pick up a troublesome station where the differences will be prominent. Of course, if the signal from the station is too poor, then none of them will pick it up decently, so it really is a narrow range of signal quality where there will be a significant difference between the three tuners under consideration.
In most cases, the tuner in the SX-450 will be satisfactory. Having owned an SX-450 for a while, I can certainly see it as a viable option (though I kept my SX-1250; I also had, for a while, an SX-750, which I also sold).
One can try to find differences in performance by doing things to make the differences more prominent. For example, one can turn the volume way up to try to hear the noise floor during moments of silence on a broadcast, though one will be having it very loud when there isn't silence. But doing that might make one notice differences in signal to noise ratio, assuming that the station is broadcasting a quality signal where they have taken care to keep the noise floor low (if they have not kept the noise floor low, then you will hear broadcast noise in all of them). But with normal listening, all of these have a decent signal to noise ratio and one is unlikely to notice the differences without trying to make them noticeable.
With the crazy prices on vintage gear these days, if I had an SX-850, I would not be looking for a higher model. If you need more power, adding a separate power amp would be the way to go.