I agree regarding the RTPI wording. I’m not in the least bit anti-British, but I still find it odd that the organisation can’t get something as basic as this right.
As you’re in a position to join either then you must have a planning qualification which, as you know, is sufficient to work as a planner- membership of either organisation is not required in order to work. Presumably your qualification is both RTPI and IPI accredited if you’re eligible for both.
From those I know who are members of one or the other (more are in IPI than RTPI, I think), nobody would say that there are major advantages to joining. There might be advantages for the organisations in having your membership fees, in that they (or the IPI at least) work on a shoestring budget afaik and do some worthwhile work on behalf of the profession. And presumably it would bolster their cause if they can claim to be speaking on behalf of a significant proportion of the profession. But I remain to be convinced of the merits of joining either one.
I’m afraid I can’t help any more than that.