To get back on topic, here is a comparison between two different function generators, both running at 50kHz. You can clearly see that, yes indeed there is a difference in the shape "quality" between them. Both are 50 ohm terminated.
First a HP 8116A:
You can see that the square wave is a very tight shape and has rise time of 6.3ns.
Next the HP 8904A:
The edges are more rounded and the rise time is ~1.7us.
You can see a good bit of difference between them. The HP 8116A is a 50MHz generator and will, in my opinion, still output a good square wave up into 25MHz or so. The HP 8904A, on the other hand, is rated at 0-600kHz for sine and 0-50kHz for square (and ramp / triangle) so it is working at its absolute upper limit. They both are very nice units and the HP 8904A is particularly versatile, but you can see that each has its application and yes indeed not all FGs are made alike.
PS: I posted a review of the HP 8904A on my blog (shameless plug) in case you might be interested and I'm planning one on the HP 8116A as well.
http://katzelectronics.blogspot.com/2015/01/hp-3904a-review.html Just in case you might be interested.
PPS: Ignore the 2kV/div on channel one. I normally have a 1000:1 scope probe on that channel and was too lazy to change it.