I'm assuming that you're talking about typical, cheap UPSes. These devices only convert DC to AC when they have no input AC or their input AC is out of tolerance.
First, the problem you won't have: You will never have double conversion. If one UPS is on, the other will not be. The UPS connected to the wall, if converting, will keep the second UPS from converting since it will have AC input. The UPS connected to the other UPS, if converting, must not have an AC input and hence the other UPS is not converting.
Since you will never have double conversion, there will be no degradation. Each UPS will produce the output it produces, regardless of what the other UPS is doing.
With the power on, both UPSes will charge from the AC that passes straight through them. The load will run on AC as well.
When the AC fails, the first UPS will start converting. The second UPS will see AC and its battery is already charged. So it will just pass the first UPSes output AC through itself to the load.
When the first UPS dies, the second UPS will stop getting AC. It will run normally, converting DC to AC just as it would if the first UPS wasn't there.
Really there are only two problems you'll have.
First, the UPS plugged into the wall might need to supply power to charge the second UPS's battery some of the time. This will almost never happen, but you do need to make sure the first UPS can handle it. If it shuts down under that load, you'll be in trouble.
Second, the second UPS might not be happy with the output waveform of the first UPS. Some UPSes allow you to adjust their tolerance for crappy input waveforms. If the first UPS is at least a stepped square wave, you'll probably be okay. But you may find that the second UPS refuses to see the output from the first UPS as acceptable. (This only rarely actually happens, but it's hard to guarantee that it won't.)
In the end I did chain an Opti 1500VA unit for most stuff, including a small inkjet. When it gives up, then everything will be off (one laptop will have a bit more time due to its own internal UPS) including the printer. The smaller APC will buy just a little more time - finally, the router and most-important computer and one monitor will be last - and it runs on a SSD so when it gets the "now" signal it does a full clean shutdown. I posted this 5 months ago, and have been using this setup for 3 months, with one involuntary full-on test, and it seems to be fine. – SDsolar – 2017-08-16T22:02:17.460