Both APC and CyberPower have pure sine wave output UPS models. Transfer times are usually not a problem for switched-mode power supplies and should be in the range of a few milliseconds for most UPSes on the market.

I'd say both are good options and at least around these parts you can find replacement batteries for APC a lot easier than for CyberPower, that is if you want to stick to vendor-recommended/manufactured batteries. That being said I currently own a CyberPower UPS, I've had APC UPSes in the past, and I'm happier with what I have right now. APCs have always felt cheaper in terms of build quality, but I guess it's down to personal taste.

Yeah today the response time is not a problem I guess, when I bought mine not every UPS had the same performance in that regard.

Another thing: you cite batteries, well batteries are standard, I mean they use existing models of batteries that can fit the requirements of the UPS they are going to build. Unless a builder decides to go for custom batteries and then you have no other choice than go for the original replacement.
The first time I had to replace them I bought the original brand name pack, which set me back XXX, the second time I went to a local dealer with a battery and asked for something equivalent, I saved a bit of money.

The sine wave is a matter we could discuss for hours: take a look at this review: https://www.custompcreview.com/reviews/cyberpower-cp1500-avr-intelligent-lcd-cp1500-pfc-sinewave-ups-review/
To him those are great pieces of equipment to me honestly they don't look very good: look at how dirty is the current as they kick in.

I chose mine because it can kick in and continue the wave form exactly where it stopped and basically immediately.

Usually the most part of electronics you are going to hook to it won't have problems but, you know, the better the current you give to your hardware the longer it will last and we are talking of years of that.

If I had to shop for a LI UPS today I would look at the performances in the first place and then to the brand.
I mean there are low end and high end UPSes in every catalog of each of the brands so before you buy take a look at those features.

True, you can always pick an equivalent one with the same capacity and voltage and save some money.

Great pieces of equipment... for their price point and their target audience. Remember these are not industrial-quality UPSes. Most user-grade UPSes (at least mid-ranged ones) will get rather jiggly with the wave form during transfer times, but hey, I don't know what kind of wave quality you usually get from the mains, but around these parts fluctuations can get even nastier than that :).