I've heard reports that the newer heat pump clothes dryers are less prone to cause shrinking. In their default mode they act more like a dehumidifier than a heater. In theory you can wash more delicate dry-clean only garments as well.
It's very gentle on clothes, but it does take a bit longer to dry.
The big difference in day to day use for us actually comes by way of the lint trap. Not only do you have to clean the lint trap every time (as normal) you also have to clean the heat exchanger every few loads. This process is a pain in the butt, you have to lie on the ground and gently brush away wet lint off the fins while avoiding bending them. The more lint that is left on the fins the less efficient the dryer is and the longer it takes to dry a load.
This will ultimately end up causing an issue long term (know idea how long) as more and more lint makes its way past the accessible portions of the exchanger and the dryer will take longer and longer. You can in theory take these apart and power wash them but it is not user friendly in the least and probably not worth the effort of a technician.
All together we like the dryer though.
(I've been tempted to just yolo buy one to try it out but installing it in my house is a pain in the rear because of the location.)