Slightly different spin: a little bit ago, I shopped for replacing my computer speakers. Mind, this is in the same room as my main rig, so SQ was not the point (yes, I wanted something that would sound 'good' when I was surfing YT or whatever, but since I don't game or watch movies on my computer nothing else was an issue). I looked at Studio Monitors knowing I needed something small due to placement issues, so that ruled out anything with good bass response (Monitors with 8" woofers, for example). I then needed to replace the Bass module of the previous Logitech 2.1 THX thing
and all the sudden I was looking at $500-700 of lower end gear to replace a quite adequate sound solution for my needs.
I decided to try the Klipsch 2.1 THX system instead. Same price and basic specs of the Logitech. Boom, done.
What you are asking us to compare for you are two completely different things, and so I have to ask: where are your values at? I won't judge you if you say you went on and got the 5s. It's your system and your ducats!
But when you say between these two and you but the Buchy system up there, well, there's no contest. The Buchardts will dominate Klipsch, Edifier, and anything else in that category.
So...
Between Klipsch and Edifier, I would get the Klipsch. I've heard them: they are OK. AudioEngine A5+ would be another in this category that I would recommend. I did shop Edifier and cannot offer anything but contempt for them.
You will want a Sub to add to these systems. They will not perform low. Mind, I'm not talking about infrasonic stuff, but just getting down low enough to enjoy action movies or whatever. Similar to the way my Logitech and Klipsch 2.1 THX systems have a "Sub" (which I prefer to think of as a bass module). For you, that would be like an 8-10" Sub that can get you into the low 20Hz range, and be able to overlap and blend into the speakers you choose. Again, not a requirement, but I know for myself, those little monitors will not satisfy the bass requirement that I would expect, on their own.
For me, I would look at better monitors... something in between the Klipsch/Audioengine category and the Buchardt category. And I would look for something that I could add a Sub in with if I wasn't satisfied with bass response.
This may be helpful to help you decide which direction you may want to go:
Cheers!