I prefer bagless in just about any situation, especially with pets. If you have a pet that sheds a lot, a vacuum with a "pet" designation, such as a Dyson Animal, is the way to go. I think pet hair will fill bags very quickly, which means more frequent bag changes, and thus burning through money. I have been accustomed to bagless and have never owned or used a bagged vacuum in my current home.
However, a bagged vacuum has worked in one situation in the past: cleaning out a fireplace. Back in my old apartment, my family owned 2 vacuums: a Eureka Ultra ESP and a Fantom Fury. The Eureka had a hose that clamped onto the bottom, then my mom would use the hose to clean out the fireplace. She said that bagged vacuums make it easy to clean out fireplaces because all of the ash is locked in the bag and makes for easier disposal. Mom, at the time, used the Fantom Fury in that apartment with 3 cats and dark brown carpet. I now live in a home with a gas fireplace, so we don't have to constantly maintain it.
When the bin is full, I take it to the kitchen trash can and empty it. I prefer to do this after every single use, regardless of how full it is. I don't like having dust and dirt sitting in a bin or bag, which can potentially rot and result in bad odors. Then I follow the maintenance instructions in the manual or on the vacuum itself to wash the filter(s) as directed. I've never experienced a loss of suction on a vacuum with two or more cyclones. If you're cleaning up lots of pet hair, a bagless vacuum is much more economical.