In the drone motor industry, there are a lot of variations in the stator sizes of brushless motors. There are several motors that have similar stator volume but one is wider and the other is taller. What are the inherent differences in performance between a drone motor that is wider stator vs one that has a taller stator with a similar stator volume? Would the stator shape influence which props it should use?
The simple answer is "more width equals more torque".
More torque let's you drive a higher pitch or larger diameter prop effectively. Given the same size prop, it will drive it with more effectiveness. Added torque allows the prop to spin up or slow down faster, which ultimate results in a better flying quad because it can more quickly and accurately respond to your stick inputs.
In the miniquad community, this is the reason a lot of freestyle pilots trend toward wider motors on a 5" prop compared to racers. It provides a higher level of smoothness because of how it reacts.
Another effect of more width is more efficiency especially with big crafts that are targeting flight time. You'll see lots of the big (15" or larger) propeller quadcopters with very wide motors. For instance a 5010 stator size. High performance isn't usually the goal here so a wider stator allows them to drive the big prop without lots of excess weight and power that they don't need.
This is an endurance quad I built years ago with the 5010 motors I mentioned. Just to give you an idea of the scale and the uses of a very wide motor.
To simplify this discussion, it's easiest to focus on a single size class for these motors - 22XX-24XX motors on 3.5-6g propellers (5"-6"). It is also incredibly difficult to decouple effects of batteries and propellers in concert with these changes.
Generally the wider stator is capable of greater instantaneous torque, and can generate a proportionately larger initial RPM change within a small time period, which typically results in faster thrust changes in response to FC->ESC commanded changes. The relative efficiency curve (when taking into account battery response) with most propellers mean that for a similar volume of stator, a wider and shorter motor will produce its most efficient thrust in the low-mid throttle range compared to a narrower and taller stator. At higher RPM, the taller stators tend to retain more efficiency, which as battery limitations become involved mean there is greater overall thrust at higher RPM ranges which effectively closes the gap for torque response, and why simplifying this into terms of 'torque' is often misleading.
There are various workarounds to changing this response - specifying higher voltage batteries and utilizing less of the available power can cover for many of these differences because higher input voltage increases the amount of instantaneous torque available for any motor configuration.
Broadly, when discussing which propellers pair best with specifically sized stators, in my personal experience the propellers with more chord (thicker blades) respond excellently and pair brilliantly with wider stators (e.g. 2306.5 and HQ V2S props), while the narrower chord props that respond through bigger RPM deltas tend to produce more consistent responses with taller stators (e.g. 2207 with Gemfan/TMotor props) to achieve a good control feel.
Broadening this discussion to other ranges of propellers & motor size, these trends persist, but quite often other factors can become more significant (in very lightweight 65mm-3" setups, battery performance and FC response can play a larger role, as can craft all-up weight. In 7" and larger quads, the wider variance in prop weight/pitch/chord/responsiveness means stators can vary widely with differing results, but significant overlap in what works well (e.g. 2212 and 2806.5 motors being able to use the same props despite disparate stator dimensions. Depending on the intended RPM range, quite often the tendency for wider stators to have a large efficiency 'hump' near the 30-60% throttle range works to their benefit. Similarly, on racing craft where the histogram of throttle percentage is often in the 50-80% range, 7-8mm tall stators (or taller for macroquads) tends to perform best.