For me the VH4 is a great jack of all trades. The classic Ch3 gets the most love, but the other three channels are underrepresented on YT. They can all sound great. Ch2 and Ch4 initially took me the longest to tweak to what I wanted and I found Ch4 was too compressed and saturated so I put a 12AT7/5751 into V2 to tame it back a bit. I tend to prefer Ch2 with a slight boost or overdrive to push it into that Marshally top end crunch. A Boss BD-2 into Ch1 can also to a great job. I find it overall a kind of compressed darker amp, which isn't a totally bad thing, but I did an easy NFB mod which opened it up a touch just nicely for me. If you've played a VH4 and found you needed some changes then...
The Hagen is a VH4 MKII effectively, to me. Same core with 20 something years of little updates and minor tweaks to a VH4 platform, without the need to overhaul the VH4 and re-release it. Ch1 clean is a bit sweeter and nicer. Ch2 has a bit more crunchy kerrang to it. Ch3 sounds just like the VH4 one but perhaps a touch less compressed. Ch4 is easier to get along with and dial in than the VH4 Ch4 was. It also has some practical updates like the switchable loop, losing the channel inserts, easier bias points and a switchable second Master Volume. I find it less compressed than the VH4 overall, maybe a little less tight and a looser feel too. The VH4 has its iconic look, but I also think the Hagen looks like a sexy bitch, on a superficial aesthetic POV
It's really hard to hear or feel the differences from video clips unfortunately, and individual choices on how they're dialled in by the operator can nullify any difference the video or sound clip might present. I acknowledge it's hard to have both in the room to directly compare, but naturally it's the best way to 100% know for yourself, if that's what you want of course. I love both amps and they're more similar than not. They both play well with others when blended of course, as many do, and typically with an amp with the higher and brighter Marshally type tonal zones.
I don't have any experience with the VH2 to comment sorry.
TL;DR - IMO - The VH4 is an iconic modern classic, with more to it than most YT clips show. The Hagen is an update on that.
Gratuitous amp porn