Perhaps the easiest way to answer your question is whether you plan to rent a car. If you don't plan on renting a car, then don't bother with the Highlands. There are some nice daytrips, but the Highlands are best explored on your own. To me, part of the Highlands experience is stumbling upon little-touristed places and enjoying solitude at some of the world's most scenic sites. Glasgow and Edinburgh, on the other hand, are best explored without a car.
I agree completely with Eirelover. The Highlands cannot be missed! Edinburgh is one of my favorite cities, too, and I have spent a lot of time there, but if tomorrow you were to put an airline ticket to Scotland in my hand, I would choose the Highlands. Others will know more about the drive from Glasgow, but as soon as I land at the airport, I would get in my rental car and head to Oban.
It is not worth going to Inverness since the "Highlands" are really about the unspoilt rural region.
That said, Edinburgh is truly fabulous. The castle is breathtaking and there is so much else to see. Plus the pubs are great.
You cannot go wrong either way. But I would not try to do both this trip. Last trip to Scotland we spent nine nights in the Highlands, including three on Orkney -- and we didn't even cover the entire Highlands.