What is better/easier to use for changing tires (or plain lifting up the
corner of a car) - a hydraulic bottle jack or a hydraulic floor jack?

Personally, I much perfer the floor jack for the use you stated. You
give up some portability, and it takes more room to store, but it's
far quicker and more convenient, you don't have to kneel down to place
it, and the jacking proceedure is easier.

But check the jack-placement points on your cars, and look at the
factory jack to see how it engages them. I've had to fabricate a
block to fit on the jack so it wouldn't crimp or crush the metal ridge
on the jacking point. It's just a 4" length of 2X4 with a slot cut in
it.

-Zz