I couldn't find API SH rated synthetic oil on the shelf. But the MINI owner's guide says "API SH or better". I am not a petroleum engineer, so I ask "What's better"?
The API SM rated oils have increased molydenum to improve gas milage by reducing friction. API SL doesn't, but both have reduced phosphorus (helps lower emmisions).
So, what's better?

 

Well, the owner's manual doesn't specify "SH or better", it actually says "SH or higher", so per the owner's manual, either SL or SM would work just fine.

As to which one is "better", that's very subjective and depends on your application. As an example, the standards have gradually been reducing the allowable concentrations of phosphorus, primarily in order to help protect catalytic converters. That's fine, but the part of the reason phosphorus was in there in the first place was as an extreme-pressure additive, to provide some "last line of defense" against metal-to-metal contact in case the oil film breaks down.

So, is the reduction in phosphorus a good thing or not? It's subjective (especially if you're talking about an older car or a motorcycle that doesn't have a catalytic converter in the first place).

 

I wouldnt go looking too hard to find API SH oil as you probably wouldnt find it. That is an old rating from 1994, superceeded in 1997 by SJ and 2001 by SL and 2004 by SM.