GJAAH is the prefix of one of the series of GXV160 engines made in China - apparently the first one to be made there. This is probably not a good thing.
You might recheck that "MAJ" you saw on the GXV140. There was an MAC and an MAD Engine Type code on GXV140s, but no MAJ.
I can't tell at this distance how the condition of those two particular mowers compares - that is probably more important than where the engines were made. As I understand it, the HRU195, and perhaps the HRU215 (19 and 21 inch versions of effectively the same mower) were particularly popular with contractors. Honda's popularity may have waned a bit since then. The GXV140 engine was advertised as 5.0 HP and the GXV160 as 5.5 HP.
You might try browsing one of the sites the mowing contractors use, and pick up some comments on both mowers. I can't comment usefully - I have an HRU195 and I like it a lot, but I've never even used an HRU196 or HRU216.