I would hope that you wouldn't see serious problems with most of the chipsets, but the worst case scenario is that a driver vendor for one of the FireWire interfaces requires some OHCI 1.1 feature. I think all TI chips are OHCI 1.1, while a great many of the VIA FW chips out there are not. (The current stuff should be, AFAIK.) The only devices that are likely to care are those that do isoch communication, e.g. audio interfaces, camcorders, etc.
AVC interfaces (camcorders, the Presonus FireBox and FP10, maybe M-Audio with recent firmware, Phonic, older Mackie boards with add-on cards, most stuff by Focusrite, etc.) should "just work".
DICE II-based gear (Presonus FireStudio, anything by TC, Alesis, etc.) probably will fall over dead like it always does.
MOTU is a question mark. They might handle OHCI 1.0 support now, but at least a few years ago, they basically wouldn't touch NEC, Ricoh, or VIA chips, and I strongly suspect this is because those chipsets lacked OHCI 1.1 support. Gut feeling.
RME apparently handles 1.0 just fine.
If you bought a recent VIA-based interface, it is probably OHCI 1.1-compliant anyway. I'd expect those to be about as compatible as TI or LSI.