I've done both...the Duomo once, like 10 years ago and the Torre 2x.(once with my husband on another trip and once with my son last fall. The line to climb the Duomo was impossible.
The line to climb the Duomo was unbelievable. It was at least 100+ people long and didn't seem to move. They only allow a certain # of people in at a time, so it moves very slowly. To avoid the line, you could buy the Firenze Card, but that is so expensive now, not worth it. We checked several times during the day to see if the line got shorter, but it never did...
The Torre, on the other hand, had no line at all. I think most people don't realize you can go up the tower.
Both climbs are NOT easy if you are not in shape. In the bell tower, just when you think you've hit the top, you realize just across the way is another set of stairs, then another set of stairs.
The nice thing about the bell tower is you get to see the Duomo....the nice thing about the Duomo is, you are a bit higher than the tower, and you can see the old city walls and get a nice 360 view of the surrounding countryside. (on a clear day that is)
Big suggestion, don't take a backpack, but do take water. Hit the bathroom before you get in line and be prepared to stand and stand in the Duomo line...2-3 hours perhaps.
Hint: the Duomo line is on the left side of the church as you face the front, go when you will be in the shade, I can't image standing outside in the sun, and plan to be harassed by the traveling junk sales people, peddling all kinds of crap. (although the police will come once in a while and "raid" That's fun to watch these guys RUN away with their junk to avoid being taken away in the police car.
If you are training, the only way to train is to climb stairs...lots of them. There are not very many places where you can rest...you will be in the way of people climbing up, and coming back down. If you are fit enough, it's not that difficult to do both in one day.