If you were behind my DM screen, how would you proceed with this situation?
Retreater
Survivor D&D! You already have the two tribes!
An interesting experiment might be to take each subgroup through a short scenario and video it. Give the video to the other group and let them see how each style works (reckless fun vs. tried and true). Maybe each group could learn something from each other.
In a way, I am part of two groups and I see a similar situation. One is a group of long-time players and bringing in new blood is a huge challenge. So many inside jokes. The group has problems (well, I think they do, but that may just be me) but change is painful. I am in their age group (greybeard) but we just seems worlds apart.
I play/GM another group that is younger, but still veteran. That group hums quite nicely. A nice balance of enthusiasm and experience.
Well, enough rambling. If you can get your group to mix, then your overall experience will be great. I do not know what will open the older group's eyes, but the enthusiasm of less jaded gamers keeps the game fun, IMO.
One other option that may backfire - change genres. If the vets are stuck in a rut, throwing them in something completely different might allow them to recapture some of that old energy. One the other hand, they might fight you tooth and nail and it all might just blow up.