Spinning vs. Running - Confused!

So, last night I decided to try something different. Previously, my main cardio workout consisted of purely running (treadmill), and maybe the occasional followup with a stationary bike or the stairmaster. However, last night I decided to try a spin class, and shake things up a little bit with something different. After taking the class, however, I'm confused!

When I run on the treadmill, I'll usually do a 5K, plus a 5-minute cool down. This normally takes about 45 minutes. During that time, my heartrate will go from about 150 (walking) to 185 (running), during the intervals while doing the 5K (I'm not in shape enough to run the entire thing yet). By the time I'm done, my face is completely drenched. My hair is soaking wet, my towel is dripping, and I'm an all-out sweaty mess! According to my heart rate monitor, I'm at about 600-700 calories burned.

Now, last night I decided to try spinning. I started out doing ok on it, spinning constantly the entire time. The first few times under a higher resistance the instructor said to stand up on the bike, as though you were pedaling up a hill. I tried a bit, but my legs started to give out on me because they were so tired, and attempting to sit back down on the bike resulted in the pedals slipping out from under my feet, and me having to reach down and reinsert my feet into the pedal straps. So, from that point forward, every time he said to stand up, I simply turned the resistance up a couple turns and leaned forward instead, to get a bit of a workout. Once the class was over and I got off the bike, I was completely spent! My legs were exhausted. However, I had hardly any sweat on me whatsoever! In checking my heart rate on my monitor, I was in the mid 160s during the lighter resistance, and mid 180s during higher resistance. The monitor said that I burned about 700 calories as well.

So as a result, I've got a few questions comparing the two with each other.

1) Why in the world would I sweat so much while running on a treadmill, but hardly at all on the spin bike? According to the heart rate monitor, my heart rate was about the same between both, and I burned about the same amount of calories. But on the treadmill, I sweat like crazy, whereas on the bike I hardly sweat at all! (And I've heard that people pool sweat on the spin bikes!)

2) Why would I have such a hard time standing on the spin bike during the session? I know that I'm not completely used to it yet, and it takes some time to build up the strength / endurance. But I'm 189 lbs, I leg press about 350-400lbs, and calf-extension about 600-700 lbs. So I've got beefy legs! But I can't seem to stand on the bike after much of the class. This carries over to real-world bike riding as well. Whenever I got to a decent-sized hill, I was normally unable to make it all the way to the top. I would have to hop off and walk the bike the rest of the way to the top of the hill.

Thanks all for any input you can give!