Any difference in on board experience in H, O, I, C, and J fare buckets?

The fare basis matters most, and the most important letter is really the 4th from the last because that defines the "Fare Brand" (Special, Saver, Flex, Flex Plus)
R - Special
P - Saver
S - Flex
F - Flex Plus

But generally speaking, H is special, O is Saver, I & C are Flex, and J is Flex Plus.

So, for HERRRUS1 (Business Saver, US to India), it's Special (R).

The only real differences are cancel/change fees which pretty much disappear at Flex and Flex Plus, and Special has no seat selection until check-in and no lounge access nor chauffeur drive. Unlike BA, you cannot pay for seat selection ahead of time, which makes it a fare that I try to avoid at all costs... unless there's zero competition with EK, the difference between Special and Saver is usually a few hundred bucks which is worth paying.