I just realized that on the scope the 12ns was for the entire rise, not half of it. So on paper numbers would be 50% for rise and fall and 50% for the flat portion of the square. Which doesn't exist on my scope.
So the better question is: Will the Agilent behave more gracefully and produce something resembling a square wave at 20MHz?
Agilent will produce signal exactly as specified. 20 MHz is 50ns for full period that consists of rise for 12,5ns , than one high flat, then falling edge of 12.5ns, and then one low flat. So each flat is also 12,5 ns for total of 50ns.
It is trapezoidal signal, which every square wave is, just to different extent.
So no it won't be better, than cheap UTG962E.
UTG962E is very cute little device that is surprisingly useful and very good for it's price.
But it is a hobby level device.
From profesional type of devices, very inexpensive Siglent SDG1000X series has much better rise/fall times at 3-4 ns .
It has 2 output channels and generally better capabilities than long discontinued 33220A.
Since you say you have Siglent 800xHD scope, that Siglent AWG can also be used with scope for Bode plots...
If you want something better than UTG962E (which is really fine device for what it is) I would go with Siglent AWG.
Make note that if you need best square wave, SDG1000X series is better in that regard than new SDG1000X+ or even SDG2000X.
These 2 other AWG are better in other regards, but 1000X series had very good squarewave specs.
If you explain more your use case, maybe more help can be provided.