I have both a urostomy and a colostomy, so I can speak to this.
I do not have any more trouble with leaks on the urostomy side than I do on the colostomy side. In fact, it's less on the urostomy. The only leaks I've had since getting my system down have been entirely my fault, mostly caused by falling asleep without hooking up a night bag. (Don't do that! Lol)
Changing appliances is a bit more challenging for the urostomy because, as you've said, the urostomy output never stops. You'll need to do most of the change one-handed so you can hold some paper towel over the stoma while cleaning and drying the skin. Some people are able to get nearly no output by changing first thing in the morning (before coffee!). That hasn't worked for me, though. So I use a paper towel and slap that wafer on very quickly. I've had some frustrating days, but overall it works out fine.
If you are having issues with your bladder that are impacting your quality of life, I think you will be happy with the urostomy. You certainly have an advantage going into it since you are already experienced with managing a colostomy. You'll pick up managing the urostomy faster.
We have other members with urostomies, but they tend to be quieter than me. Maybe someone else will chime in. But if not, feel free to ask anything.