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Different brands of mouthpiece manufacturers have different ways of naming the size of their mouthpieces. Is there some kind of common convention, like letters being the depth, small numbers meaning small width, and the like?
Bach's 1-1/2 C seems to match Yamaha's 16C4 according to this page, but I'm more looking for a way of comparing without looking up in a table.
The only "convention" as such that exists, is that lots of manufacturers happen to use Bach's sizing numbers (where a smaller number = larger diameter and the letter refers to the shape of the cup), if only because Bach is so ubiquitous in the brass world.
Here is a rather extensive chart:
http://www.allbrassradio.com/tmptmpccharts.htm
Both Schilke and Denis Wick have mouthpiece comparison charts:
http://www.schilkemusic.com/files/SchilkeMPChart0207.pdf
http://www.deniswick.com/images/stories/mouthpieces/mouthpieceComparisonChart.pdf
However, different manufacturers vary greatly in rim width/shape (not diameter, which is what is generally communicated in the 'size'), and that can have a much bigger effect on how the mouthpiece feels.
I find the best way to compare mouthpiece is to look up each individual manufacturer's product listing--Most have a comment of some sort that categorizes mouthpieces as being good for high range, open sound, free blowing, 'symphonic favourite', and the like.
No, there is no general convention, or international standard, or anything remotely like that. Even manufacturers that publish charts of how their pieces compare to other brands don't always agree with others. The problem is, every maker seems to measure things in slightly different places. For example, cup size can be measured at the very first start of the dropoff into the rim, or further down the curve, or at the place where the cup itself "starts".
People also come to different conclusions themselves about which piece feels bigger or smaller due to the shape of their own teeth and facial structure.
Even worse, some mouthpiece makers are notorious for huge variations in the sizing of their pieces. Bach is notorious for this with their mouthpieces. You can pick up 3C examples from the 60s, 70s, 80s, 90s, etc., and have them all vary wildly in size. In fact, sometimes they vary even within production from the same time period.
Most modern makers use CNC equipment to make them now and consistency is much better of course.
Another thing to be aware of is some makers use very similar labeling, like Schilke and Yamaha. They both might make a 13A4A, but they would actually be considerably different dimensionally.
The only real way to determine what you want to play is try them for yourself, unfortunately.
