I'm afraid I have to disagree. Perfectly illustated by the Freespace Films picture (the Legacy cinematic one) the broad shapes of the classic Behemoth and the Hyperion (which is the only one of these cruisers we know 100% for certain is a Behemoth lorewise) have far more in common than the Hyperion and the Minotaur. For one the Minotaur has an elevated bridge section that widens out, the Hyperion and classic Behemoth it is nestled into the rear engine section.
In addition the Hyperion and Behemoth, the engine section extends backwards from the wings, whereas the Minotaur it is more level with the rear of the Wings. The Minotaur's wings and hammerhead also swoop downwards more whereas the Hyperion and Behemoth are more level.
The Minotaur's neck section appears to be semi hollow/framelike, with the Yamato cannon visible whereas the Hyperion/Behemoth is solid.
The Minotaur has laser cannons mounted along the neck, whereas the Hyperion/Behemoth they are clusted on the hammerhead (which fits with descriptions of the Behemoth class) and the hammerhead opens when firing the Yamato cannon.
And this isn't even to mention the variation in the size of windows on the Hyperion and the Minotaur (there are windows visible on the in game one) which suggests the Hyperion is far larger than the Minotaur)
In short, for the reasons I've stated the Hyperion looks nothing like the Minotaur, but very much like a higher poly, more detailed SC1 Era Behemoth. And it's only true that all BCs use the same model in game, as in story mode as I have shown previously and provided images of, Minotaurs (and Wraiths and Ravens) do appear in Storymode cinematics alongside Behemoth classes using the Hyperion model.
As for Mengst and Warfield, well there's nothing to indicate that the Dominion simply scrapped all their remaining Behemoth classes, and it's not impossible for an older class of ship to still be used as a flagship. Consider that all the points I mentioned suggest the Behemoth is bigger, and we know from the novels the Hyperion itself is more spacious than a standard Behemoth as well, so it's even likely that Mengst would have the biggest ship in the fleet as his flagship. It's certainly lavishly decorated the observatory we see. Add to this that if you look at the talk page for the Bucephalas, there is a discussion about the complete lack of any evidence that it is a Minotaur class. Given that it uses the Hyperion model I'm inclined to think it is a Behemoth class.
Concerning Warfield, well the unit for when his battlecruiser crashes is called the Helios. Even allowing for different names in the editor, we never see Prince Valerian on the surface of Char. When we do talk to him in the Char missions he seems to still be on his battlecruiser, seemingly suggesting Warfield transferred to another ship at some point before crashing on Char in the Minotaur Class Helios.
So no, in my honest opinion from my own observation of the models, I don't think I have it backwards. However I can see we'll never agree on this so I suggest we leave it as it is as we have both made out views abundantly clear.
As an addendum concerning the Marine and the Firebat and such, it is apparent from interviews with the art team of SC2 that they do consider previous graphics when designing the SC2 versions. It is a mixture of art evolution (such as the Zerg being less smooth and, to be honest, boring IMO) and in universe evolution of design.
Sometimes they feed each other, for example in the StarCraft Manga a Viking Prototype is shown called the Wyrm which uses an earlier concept of the Viking and makes it an in universe early design.
I also recall concerning the Marine specifically that on the behind the scenes DVD of WoL they mention that they were keen to preserve recognisable design elements from the original game sprites, moreso than the cinematics. Hence the SC2 Marine having the oversized, Team coloured pauldrons (for example) and let us not forget the oversized codpiece! =)
With the Firebat and Marine, perhaps the armour numbers designate a role, for example the CMC300 designating Marine armour and CMC660 designating a Firebat, even though there has certainly been variation in both, with some such as the Marine not changing much and others such as the Firebat changing a great deal?