It is hard to say what you have, although I suspect it may be a JinBao. Especially if your horn is from eBay as a discount model or from one of the JinBao distributors like Mack Brass, Wessex, esp.
Concerning the size: Many manufacturers use the Bach numbering system, of which this is one. "1 1/2" is a general bass trombone size that means roughly 28.2mm in diameter (of the inner rim). The "G" in the number specifies a particular depth. However, Bach pieces are quite variable. Two "identically" numbered Bach pieces may be different. Companies that are not Bach may simply just make a piece numbered "1.25G" or "1 1/4G" with no relationship to any Bach piece. They also may make a copy and/or a copy with slight alterations. Faxx is an example of a company that took particularly good copies of Mt. Vernon Bach mouthpieces and sells those copies. Shires is another example of a company that took copies of Bach mouthpieces and reproduces them.
Measuring the rim of a mouthpiece is not always useful. Each manufacturer (and even within manufacturers) has a different rim profile (shape of the rim as it meets the inside of the cup. How steep this profile is can make a big difference on how and where the diameter is measured. So two pieces that are 28.2mm in diameter may feel very different.
In short, I would suggest playing whichever one works better. The unlabeled one may have the silver peel if it is a JinBao. I've known a few who had pieces from them that didn't last long. Then again, it may hold up. The JinBao instruments seem to be pretty variable in quality. Some are great and others aren't.