I do somewhat agree with what Terry says, but I've mentioned that I can hear a difference between not only Bb/C and Eb/F saxophones, but I can also tell the difference between high pitch and low pitch instruments.
Taking it in reverse order, Paul Cohen demonstrates the pitch differences between HP and LP by playing two Evette-Schaeffer sopranos, that were separated by a few serial numbers, on his Vintage Saxophones Revisited CD (buy it, BTB). In my opinion, the HP horn sounds a bit sweeter than the LP one. BUT, this is just my opinion.
As far as Bb/C goes, I do think that the C melody tenor, for instance, has a much more reedy/bassoonish tone. As for Eb/F, I think that the Conn-O-Sax has a much richer tone than an equivalent Eb alto. However, in both cases, I've heard the instruments played like their Bb/F brethren and particular ranges of the C/F instruments sound, to me, like the regular Bb/Eb equivalents.
Venturing an opinion, I think any difference in tone may be due mostly to how the user is playing the horns and the mouthpiece that's being used. In the case of the F instruments (as an example), particularly the Conn-O-Sax, you've got a mouthpiece that's smaller than an alto and very similar to a Bb soprano AND you're probably using the original Conn mouthpiece or one of the contemporary copies. Additionally, you're holding the instrument in a considerably different way because they're shaped differently. It makes you want to play differently.
Bottom line is that when I listen to Paul Cohen play a Conn-O-Sax, it really does sound like a different instrument, most of the time. When I listen to Rob Verdi play it, it sounds more like a regular Eb alto.
YMMV. Hey, I've also been tested and can hear frequencies a bit higher and a bit lower than most folks. Might be those subtones/overtones than make the difference for me.