The 360 is the less robust of the two. It was designed as an 'econo' bike motor unfortunately. And, AFAIK, there never really was any kind of aftermarket 'hot-rod' stuff for the 360.
The primary weakness was the fact that the cams ran directly in the aluminum of the head, rather than in any bearing. So, dirty oil or oil starvation could ruin the entire head. That being said, MANY bikes, not just Hondas, did that and none had a real problem... I mean, if you don't change or check the oil, ya get what ya get, IMO.
The early models had cam chain tensioner problems too. There was a recall, and later models were OK from the factory. If there is what looks to be a center-punch mark around the engine serial number, it has been repaired.
Another problem is that several pieces (cam tensioners included) are no longer available from Honda and not reproduced by anyone at all. It can be VERY difficult to get new tensioners if your motor needs 'em.
The 360 is also prone to cracking the top triple clamp, as yours had. Something about the way they needed to be tighted that was not intuitive, and most of the time the owner broke it. It can be a challenge to find non-cracked parts, cause 'everyone' needs one...
Anyway, that's my two cents...
Good luck with 'em, and by all means, post up pictures!
Kirk