I think it's the power section with the APM that does it for some people. On the RH450, it gets very loud but it does it in a way that some might not appreciate. On the Blacksmith however, which has the exact same preamp, that thing is capable of some very serious output such that it wallops before the APM really starts doing it's thing. Still the APM is not what many on this forum have accused it of being, and even on the Blacksmith at lower output settings it is shaping the tone and response of the head in a way you either like or don't like. I love it personally, but wanted a little more punch on the attack which is what both the RH750 and the BG250 have, even over the Blacksmith. The Blacksmith and the RH450 are more identical in the APM implementation in that the max output of the head and the burst capabilities are set to be identical. On the RH750 and BG250, the APM is opened up a bit to allow more transient attack, which IMO makes them sound even more like a legit tube head, slightly punchier, but still with some control. Very cool to me.
As much as I loved the Tone Hammer 500 and the pedal for their tone, neither have a tube feel to me at all. They sound very warm and aggressive in the mids, and would break up well with the AGS if you drove them, but there was almost no tube-like sag in the feel or response on the head at all, which for me at least hindered the ability to play it like a "rock" head on the gig. Things you could normally do with a P bass for example just didn't work with the TH500 at all because the head didn't respond and breath like a tube head or for that matter something with a bunch of MOSFET's in the power section like the DB750 or Mesa Walkabout. The TC heads IME let you get that same kind of feel going on. You can get a little crazy with your technique, and instead of it coming out like a punchy mess, it kind of dips and sags such that comes across as very musical. Hard to explain what I'm trying to say, but if you have ever heard Mutemath's self-titled album, it is full of that kind of P-bass thing. Very loud, very driven, lots of 'sliding around' on the strings and grabbing octaves in a way that only a tube head can let you pull off in the same way. It's fun to play like that in the right setting...didn't really work with the Tone Hammer for me. YMMV.
FWIW, GRoberts had me really looking at the Orange TB500 a couple weeks ago, which I still have not tried. I did read the BGM article and listened to a lot of clips. I was thinking of picking up one of those instead of the RH750, but one thing that scared me off was that huge burst rating which is quite impressive, but I don't think it would let me accomplish what I just described and might actually work against my goals. I really don't want a tube-sounding head to have a big burst rating. I want it to compress and breath a bit when I slam it.
Anyway, a bit of a derail here. The ML112 is what lead me to finally pick up the RH750. The Tone Hammer is a good choice for that cab, but I'm looking for something a little more. I might have to try the Valkyrie also. The ML112 is working out great for me so far, and if the RH750 is a slam then I'll be buying another ML!