I am not sure I see the what exactly is the ethical issue. You need to be very honest and very clear - you are writing a paper not for yourself but for other people to read and understand, so that should be your first priority. Write something like this. "We prove property P. This result is strongly related to the result in [..] which proves property P' and extends it in the following sense ... Let us note that in all cases our property P is at least as strong as P' (see Thm~?), while in some special cases our property P favorably compares to property P'. Below we give some examples which emphasize the connection."
If the matter is easy - work out carefully some examples right in the introduction. If this is more delicate as it seems to be the case, make a new section where you can work out several examples so the reader can see that P' is saying in some cases P' implies P', while your P is saying something stronger. If you stick to math, no one I can think of will get upset over this, and there is no need to make short broad characterizations in the introduction which might upset somebody. At the same time you "besting somebody" will come across in exactly the way you desire. The only downside of this approach I can see is that the paper might get a little longer due to this examples section. But so what - the reader will appreciate the clarity, and an extra couple of pages cannot possibly affect the publication chances.
