Climbing is different from typical gym workouts. It puts far more stress on your tendons than your muscles, and tends to exert injurious forces on your muscles when it does work on them. Tendons take longer to heal than muscles.
Plus, most climbers have a series of rapid warm-up and cool-down cycles -- climb, stop, belay, climb, stop, etc. -- which doesn't get the heart rate going the same way that an extended aerobic workout does.
Your climbing will tend to improve if instead of climbing a few hard routes, you climb a bunch of routes about one full grade below your maximum ability. Bonus points if you can score a belayer that doesn't mind the boring end of the rope for an entire evening. As your muscles become fatigued, your body will start trying to get lazy and sloppy, and that's where your technique will actually improve. Straining on a really hard route doesn't do anything good for technique / body position / etc.
(Former climbing instructor from Livermore. I really miss it, can you tell?)
I climb everything from 5 grades below my current level to one grade above. I have found that consciously maintaining good technique on the hard routes helps me out a lot. I don't believe in "redpointing," so I usually don't try to force myself up a really hard route that I'm having trouble on. That is how you get injured.
The soreness I get after climbing is the same kind of soreness I used to get during the first two weeks of a weight lifting routine. It is not tendon damage or severe muscle damage because it doesn't last more than a day.
My workout guarantees I am perpetually sore. It sucks for a couple weeks, but after a few months you get used to it and you actually do have more energy... though paradoxically require more sleep to recharge. As long as I hit the minimum number of hours, though, I feel like a million bucks.
