The only issue I have with TEMA vs Sec VIII (Div 1, UHX) is the thickness of baffles. Regularly, I know that a thinner baffle is acceptable, but the customer wants TEMA R. I quote TEMA R baffles, and I get undercut by another fabricator. Sometimes I swear that they are using thinner baffles and not telling the customer. Maybe I'm just paranoid.
Just one thing, though: I've been told by a more senior engineer that many of the TEMA Mechanical Standards are only "recommendations". An actual design needs only to be close to the Standard. It seems to me, then, that "meeting" TEMA Standards is different from "meeting" the ASME Code. Does the TEMA Standard make a clear distinction between "recommendations" and "requirements"?
TEMA standards are generally minimums and cover things particular to S&T exchangers that the Code does not. They do not carry the force of law as a Code does, but...
If the client requires that a design meet the standards for some TEMA class, then to my mind, they are requirements, not recommendations.