Also note that Edinburgh airport has direct bus service to Glasgow every half hour with no changing needed, so it's easy to fly to Edinburgh and go right to Glasgow (or, or your way home, to go right from Glasgow to Edinburgh's airport).
The converse, however, is not true. From Glasgow airport, you have to go into the center of Glasgow, to change to a bus or train to Edinburgh.
Both cities have plenty to do for a few days, but they are as different as Baltimore and Washington DC (two other cities that are close in distance, but not in any other way). If the cost of flights is not a factor, look at Rick's Scotland or Great Britain book, to see if one appeals to you more. Each book has the same excellent chapters on the two cities.