You will probably get a lot of great replies but I think the main difference is that the KS60 will yield a better cut in some materials (certainly better off cuts) and will handle smaller trim pieces better.
But for framing I don't think I would use the KS60 much to be honest.
On my two recent decking jobs I decided to do all the framing and ended up doing the decking with track/short track saws. That included stair stringers and posts. For the stringers I made a very simple jig for the track saw and cut down all the triangular pieces just as fast and as accurate as with a mitre saw and more comfortable I would add.
Currently running a studio build with NO mitre saw on site. I am cutting frames, trim pieces and sheet goods to size with "just" a HKC55 with the short FSK250 short track (which I prefer) and I have a 1080mm and 2700mm rail for sheet goods and ripping cuts.
I have yet to miss a mitre saw and when it comes down to the subflooring and laminate I can still do without a mitre saw.
I actually run Mafell track saws normally but for this particular job I have switched gear with a colleague to use his 2700mm guide rail for framing and sheet goods (have some 70+ sheets to cut...) for a few weeks.
I have grown to like the HKC 55 though I think it is pretty weak when it comes to ripping soft wood studs compared to the Mafell KSS50 - and I am using the 12T Panther blade for ripping so using the "correct blade" for the task. I guess (and hope) the corded one rips a lot better. Still, it gets the job done and there isn't that much ripping involved - still would not be able to do it with the mitre saw and it also saves me from having to bring a table saw to the site so all in all I think it is super to have that HKC replace both a mitre and a table saw on site for this particular build.
I don't know how extensive your build is but in my case it is a little bit of everything: en empty space in that is divided up by walls and podiums to be built, ventilation ducts to be covered up, flooring etc.
I get by just fine with the HKC 55, a Jigsaw, a Multicutter and a japanese hand saw. It feels great to just walk in to an empty space with just a bundle of studs and the HKC55 and a few hours later there is a stud frame in place and very little gear to haul around.
When it comes to the finishing trim and some bespoke furniture most of it will be made at the workshop and once everything is in place I might clear out all the other gear and bring a small mitre saw for the last trim.
Lengthy answer, hope it helps you out a little.