He probably need to refresh his oil knowledge.
A lot has changed since the 80s.
Our bike can take mineral, semi and synthetic without issue depending on your usage.
Semi and Synthetic basically increase the life of the oil, In theory you can replace them less often.
Our Honda dealer in NZ used Motul 5100 for all their servicing which is a semi synthetic oil.
I used Motul 7100 which is full synthetic recently and it seems to make the engine run smoother.
The full synthetic oil also seems to have better resistance to heat which may contribute to the extra smoothness when I went from 5100 to 7100.
Here's a nice write up on Honda oil by Honda Canada
The GN4 which I suspect is what you get from most dealer in America is Mineral based oil (not semi synthetic and not synthetic)
This is their "entry level" "general purpose" oil
Then you can get HP4 andHP4M which is semi synthetic (equivalent to Motul 5100)
All the way to HP4S which is full synthetic (equivalent to Motul 7100 or maybe even 300V (this is the top of the range on the Motul range)
To answer your question, which one is better?
Make sure you have the right weight 10W40 too heavy 10w50 and it will mess with your CCT. There has been report of CCT failing or becomes noisy by people running heavier oil.
Mineral V Semi V Full?
Depend with your usage and how much you want to spend.
If you live in easy climate (not too hot and not too cold) and only use it for road use without staying at the high RPM for too long. Mineral is ok Semi is better.
If you ride at high rpm a lot (e.g. track use) or live in hot climate (temperature above 30 degrees celcius)
Go with Semi or Full Synthetic.
For track bike that get the oil changed more often (ever 1 or 2 track days)
Theoretically you can run mineral as you will change the oil before it has a chance to break down; but for the small price difference of semi synthetic why not go the extra little bit.
I hope this helps and if there is anything that I may have gotten wrong, feel free to correct it.