Not even remotely close, I'm pretty sure. I was in Edinburgh in April of 1998 when they both fell on the same weekend. Edinburgh was Saturday and the Old Firm Sunday. I was busy being a tourist on Saturday, but I got absolutely no sense of a buzz in the city about the game, although it was a sell-out at Easter Road. Of course, low 30s and snow showers probably had something to do with it. On Sunday, there were a lot of pubs filled with people watching the Old Firm game on TV. In the one I wound up in, the most popular sentiment was that it was too bad there wasn't a way they could both lose, but everyone was watching. Somehow I doubt there was anybody in pubs in Glasgow the day before watching Hibs and Hearts.
The intensity is about the same (without the same amount of hatred though) but on a much smaller scale i.e less people support hibs-hearts than celtic-gers.
Thanks Scottish Morton and NER. When my wife and I visited Edinburgh (mid October) on our honeymoon, I didn't see one person sporting Hearts or Hibs attire (kit or scarf), nor in the 2 days of visiting 3-5 pubs do I recall any loyalty to either Edinburgh club.
What?!?! I was at the Edienborough Derby in August at Easter Road. The intensity was great. Hibs won for the first time in a long time. Probally nowhere near the Gers Celtic games, but a great scence none the less.