Unless your PSUs are from the early 90s, Sine or Square AC does not matter for computer applications, as it would get converted in your switching supply to DC right upon entry, and then further converted to something the unit can work with.
PCs, monitors, TVs, Printers, cellphone, and other chargers are all using internal switching power supplies due to those being cheaper and by far more compact than older transformer supplies. Sine or Square does matter for capacitive and inductive loads. AC motors (vacuum cleaners for example) and low-frequency transformers (such as the ones in microwave ovens) suffer and excessively heat up from sharp rises and falls found in Square and approximated sine wave power sources. Even Microwave ovens are slowly switching to Inverter type... Good audio equipment is still using transformers too due to noise with switching stuff.
As for UPS types, they differ by switching time, efficiency, build quality, size, battery capacity (for those with batteries as opposed to external battery hookups which IMHO are better). Every UPS is a power inverter with battery, battery charger and feed-switching circuit. Most recent low-power ones (3kw and under) use HF boost to get high voltage DC from the battery and then create AC using PWM or SPWM. They are smaller and lighter. Older UPS and most higher wattage use low-voltage high-current SPWM to drive a low-frequency step-up transformer, they are more durable but at the same time much bulkier and heavier (3kw would be about 10-12kg), and cost a lot more than HF. Just to give you some figures, 3kw 60Hz 8v:120v transformer alone is about 8kg and costs around 500$, while 3kw 30kHz 12v:120v weights 1kg with packaging and costs about 100$...
Another concern with all switching PSUs including the ones inside UPSs (and anything that is driven by PWM in general) is the power factor issues (current spikes, and reactive loading). And again, it is well treated by either passive (better but expensive) or active (innovation to make it cheaper) power factor correction. That is what you read as PFC on your labels... Cheaper passive filters contain inductors that can create high-voltage spikes with load changes, especially strong if the supply device is rated for high load, which will trip some devices like in the case with ONT. Many surge protectors will trip too. If your UPS costs less than 200-300$ excluding battery cost, you only get what you paid for, do not expect to find fancy input/output filters.
Not to be offensive but this entire thread is full of bias and myths... I will be building one of those inverters soon for my electric dirtbike charger, will maybe post some build results here and provide some theory wrap