We have boston ivy growing on the east side of our house. What makes it look so thick, is multiple stems growing up. You can work at the base and cut some of the stems there, then pull the whole stem off the fence. It is shocking and messy, but it doesn't take long for it to fill in when the stems underneath can get some sun.
Or, start at the top and pull stems off all the way to the bottom.
Our house usually keeps a pretty thin growth as it is tall, and the wind prunes it. I do have to climb up on the ladder every summer and pull it away from the eaves. The ladder is at its tallest extension--not my favorite gardening chore!!
Boston ivy is deciduous; the leafless tracings of the vines on the house are kind of interesting in the winter.