Hmm, I've played all the Diezels and owned a few. I currently have a Paul.
VH4 - It's the oldest running of the Diezel line. I do think it's kind of crisp and classic but also kind of hi-fi. It has a lot of low end, but manageable. I have a harder time dialing the low end on the Paul and Herbert. The way the mids stand out I suppose would be why it's said to be popular as a studio amp. There was one at a local Jackson dealer near my house which I used to play all the time. It was good at any volume. People say they like the 3rd channel, but I think all of the channels are equally good. I also think the channels are quite differently voiced. By the way, it was the 100w model which I think is the Vh4S. I think the other model is 180w like the Herbert.
Herbert - Lots of massive low end, hi-fi, punchy, one of my favorite for lead tone. Andy Wood uses one, and if you check out his album, it sounds damned good. I think it can sound Marshally kind of like a Silver Jubilee in a way, but I wouldn't characterize it as a Marshall sounding amp. To me there's kind of a smoothness to it that the Hagen and VH4 don't have.
Hagen - Probably the most overlooked for what it offers. In my opinion, it's the most versatile of all Diezels. The clean channel is magnificent, but of course all of the gain channels are. It's kind of more hi-fi and modern than the VH4 or Herbert. For some reason, and I can't quite articulate why, but it reminds me a bit of the Einstein. I had an Einstein once and regrettably sold it. For whatever reason, the Hagen kind of reminds me of it. I don't know if anyone else thinks so.
D-Moll - It's a very versatile amplifier. Great clean tone, but less feature-rich than the other amps because it has 2 main channels, and the third channel is kind of an extension of channel 2 and shares the channel 2 EQ. However, the 3rd channel is voiced differently and has more gain, so it's pretty damned versatile. The D-Moll (apparently kind of named after demon) has a really great mid contour knob. To me the D-Moll has kind of a different breakup than the Hagen or VH4. I don't think it sounds like the other Diezels, but might have some resemblance to the Herbert to some people. Channel 2 is brighter than channel 3, channel 3 is still present but with thicker lower mids. Channel 2 also feels a bit tighter, but that might just be because it doesn't get as gainy as channel 3. The "liquid" lead tone people talk about, it's in every Diezel amp, and the D-Moll has it.
Paul - Much of what I said about the D-Moll is true for the Paul. The Paul is a bit brighter and crisper overall. It has digital reverb instead of the mid contour of the D-Moll. The reverb is very good and you can turn it up high without it getting in the way of your tone. The clean channel is very much like the D-Moll, but crisper or spankier and therefore more appealing to the Fender kind of crowd. Channel 2 is brighter than channel 3 with less gain. I find channel 2 to be perfect for metal rhythms with the gain maxed. Channel 3 has liquid sustain at around 1:00, so you'd only have to go past that if you have weak vintage pickups or single-coils perhaps. You probably never have to max channel 3 gain. The Paul has a massive low end and harder to dial out than the D-Moll. The way the clean channel breaks up is extremely appealing, so most people can probably just live on channels 1 & 2. I think the Paul is a little more aggressive than the D-Moll, and I think the D-Moll is capable of a bit smoother tones. The way the Paul breaks up is similar to the D-Moll. A couple of people have said that the D-Moll has kind of a fuzzy or looser breakup, and I can kind of see that, but Paul is sensitive to playing dynamics. If you're precise in your muting techniques it's plenty tight. The D-Moll is kind of like that too, but the Hagen and Herbert seem easier to get tight, percussive palm mutes because they're more compressed.
Lil Fokker - Even though they don't make it now, it wasn't long ago that they discontinued it and there are still many around for the buying/trading. The Lil Fokker has an outstanding channel 1 which goes from clean to classic rock. Even though it's not really a crisp amp, somehow it pulls off incredible clean sounds. Channel 2 is massive and can get very saturated. It may be the easiest of all the Diezels to dial in. It's a damned shame that they stopped making it. I wish I had one next to my Paul. If they just made it a little smaller then I'd still have mine.
That's my take on them. You'll find that a lot of people have differing opinions. Some will say one amp sounds like some channel on another, etc., but I think they're all quite unique. The VH4 may be the most popular and oldest, but I see the Hagen as the flagship amp for Diezel.