I visited both systems on a quick trip to western Canada a few years ago.
Calgary's system is larger: a downtown spine along a surface street, and three branches stretching out to the northwest, northeast and southeast. The scenery is varied, with sections running in expressway median, boulevard median with shopping plazas on both sides, cutting through residential neighborhoods, etc. Coming towards downtown from the northwest and northeast you get some nice views as you descend into the river valley. However, there are no significant underground sections, just a few short tunnels, and no underground stations.
Edmonton has a single line that runs underground through downtown. Each of the underground stations has a distinctive style, not the same cookie-cutter design for all of them. The northern section runs along a freight railroad ROW. The river crossing is rather spectacular because the valley is deep and the LRT shoots out of the riverbank on both sides (underground sections) to cross on a long bridge. An extension to the south is under construction but I don't think it's open yet.
Edmonton has a few other attractions. There's a heritage trolley line (the High Bridge line) that crosses the river on a former railroad bridge not far from the LRT crossing. Another one carries people around Fort Edmonton Park. Both run only during the summer.
And Edmonton has one of the few electric trolleybus systems in North America. It's in serious danger of being abandoned in the next couple of years. Upper-level transit management and city officials are actively hostile to the trolleys, which still run mainly because of pressure from city council, fueled by vocal pro-trolley citizen groups. But the vehicles date from the mid 1980s and need to be replaced soon. City council ordered a trial of a modern low-floor trolley with battery backup power. Vancouver has loaned one of their newly-acquired trolleys, and it should go into revenue service sometime soon if it hasn't already. So if you're at all interested in trolleybuses, it would be a good idea to visit soon. The whole system could shut down as early as next year or maybe 2009, as I understand it.
You can easily visit Edmonton from Calgary even if you don't have a car, because there's frequent bus service (Greyhound and Red Arrow). You could even do it in one long day if you're pressed for time: take a morning bus up, spend the afternoon riding around, and take an evening bus back.
I visited them as part of a quick circle tour: I flew to Calgary, took the bus to Edmonton, then the train to Vancouver, and the bus back to Calgary, then flew home.