Also, be careful if both UPS feed from the same mains fuse. I have seen offline UPS pass dead shorts straight through and blow upstream fuses. Even worse if ampacity of the mains line is overcommitted (eg two 3000VA capable units from a 230V 16A line ... do not do that!*). Luckily, it seems that server PSU makers have by now gotten wise, it has been a long time since I have seen a server grade PSU short out its source (have seen so in the past esp with 3U/4U servers using commodity ATX PSUs).
*EE basics for server people: Volts times Amperes gives you VA. Which is close to Watts but not exactly on an AC system (pretty close if everything has good PFC). If you have to care about the difference you are operating too close to the limits anyway. Also, loading a UPS to a significant percentage of its rated output gives you short runtime.