This question came up again on an Internet forum that I frequent and since it's often asked, I thought it made sense to repeat what I posted there.
It's really an excellent question. While the difference in the exit diameter is apparent, the difference in performance can be less straight forward.
We focus so much on exit diameters, understandably, since that's the easiest way to discuss chokes. that we sometimes lose sight of what really makes a choke perform in a certain manner. It's really all about the internal geometry of the choke tube.
Every choke designer has his own idea of what makes a good design. He may have an idea of just how long a parallel section should be, how steep the angle should be on the conical section, if it should have several steps, if he should use ports to grab the wad, slow the wad or just for cosmetic effect. There are many more decisions to be made but you get the idea.
The designer should look at performance with different shells from different makers and different sizes of shot. That complicates the job but it's necessary. He must also consider how each design performs in different shotguns with different barrel lengths.
Lastly, he must consider what the general public perceives from their past experiences with chokes and shotshells.
Now to try and directly answer your question:
There can be real difference in performance in one maker's .650 and that same maker's .660 chokes.
There may be very little difference in that makers .650 and another maker's .660 choke...due to the differences in the internal geometry of the two chokes.
Not all that long ago, I evaluated 32 different chokes through 6 different guns with 3" WLB shells with 1 3/4 oz of #6 shot. I fired 3 WLB shells through each choke and gun. Choke exit diameters ranged from .643 to .676 with many "stops" in between. I then performed the same evaluation with 3" Hevi-13 shells with 2 oz. of #6 shot.
When I examined all of those patterns, looking not only at numbers of hits but also at the quality of the patterns, it was easy to see that one maker's choke with, let's say a .660 exit diameter, compared very favorably with another maker's choke with, let's say a .643 exit diameter.
So, to recap, a .650 and .660 from the same maker may pattern quite differently but a .650 from that maker and a .660 from another maker may pattern very much alike.