My advice is not to mediate (do meditate though - that's great
)
It's very flattering to be asked, and I'm sure that it is because you are a kind and thoughtful person, but unless you can be truely impartial AND are a trained and experienced mediator you could end up damaging your relationship with both of them as well as failing to resolve their issue.
If they want a mediator, then I suggest they pick an impartial professional (i.e not one of their therapists or a friend). If not then you will have to leave it up to them to sort it out. Like you said, they are grown-ups and if they want to sort it out they can. They don't need to drag all their friends into their drama.
Like the da1phrophet I had a similar situation with 2 friends not getting on (not as bad as your situation). In the past I would have rushed in a tried to fix it, but I have now learned my lesson. I did what the other poster said, told them both that I loved them and valued them, that I refused to take sides, and I refused to listen to them slag the other off. I didn't make any special arrangements for them. If I had a party I would invite both and leave it for them to sort themselves out.
Eventually, they had a heart-to-heart and although not the best of friends they have found a way forward together.
Incidently I found that getting dragged into someone elses theatricals in the past meant I was ignoring very important things of my own that I had to deal with. I'm curious to know what this argument between your friends is distracting you from in your own life?