To me, the biggest advantage of free standing tents over trekking pole tents is convenience. Once you assemble a trekking pole tent, it is a pain to move it. You can do it, but it is just a lot harder. I still prefer using trekking pole tents (because they tend to be lighter and stronger) but I miss the convenience of the free standing tents. Basically, I spend a lot more time scoping out my spot, to make sure it makes sense. I now use a clear plastic tent footprint for that purpose. With a free standing tent, I can just pick the whole thing up and move it a bit if I discover something about the original location I don't like.
To add to the inconvenience, a lot of trekking pole tents work best in one direction (relative to the wind) while many free standing tents do not. This means that if you have a bit of a slope, you may be forced to sleep at an awkward angle (e. g. a slope from left to right) to avoid the wind hitting you from the wrong side.
One last advantage to free standing tents is that they tend to be tolerant of stake (AKA peg) failures. You can have a dome tent supported by one stake. If you are in the tent, you can usually get by with all of the stakes being out. With a free standing tent, generally speaking, you are in trouble if one stake comes loose. Of course, if it is really windy, then you will want to use guy lines on a dome tent, in which case you are in pretty much the same boat as the pole tent person.