Based on interviews, the developers themselves noted that the heavy focus on z-axis animations (in particular, Ivy) was problematic.
I think Soul Calibur is a more ambitious System 12 game than Ehrgeiz and Tekken 3.
I'm not sure about Ehrgeiz, but with Tekken 3, have you looked at the actual arcade version?
PS1 port was some downright wizardry, but still had downgrades aplenty.
I'm guessing potential PS1 port of SC1 would lose the 3D backgrounds and drop to 30 fps.
Also, one other thing - you mention the arcade OST and the fact that Dreamcast version had it intact but streamed.
Fun fact: The whole game sound data took 512 kB for sequence/program and 8 MB for samples (this also included all voice overs/SFX, so actual music took even less than that) while the Dreamcast port's has massive (for the time) 450+ MB (due to using 16-bit 44kHz PCM). I have to wonder why they didn't port the sequences, as actual System 12 sound hardware was inferior to AICA (32 PCM channels, vs AICA's 64). I'm guessing space was less of an issue with GD-ROMs than the time it'd took to port the sequence data...
(Dead or Alive 2 is even weirder - Naomi version uses sequences, while the Dreamcast has ADPCM streams, even despite both games using the same sound hardware. Might be due to larger RAM pool on Naomi)...