It is impossible to pick my favorite. I love both civilized hot springs and wild hot springs.
Civilized Hot Springs are often times packed and require reservations in advance. Although you will not necessarily get that "one with nature" experience compared to wild hot springs, having a warm towel, a restroom, and a changing room is a huge accommodation. I don't ever mind a changing room when when it is below freezing! One of my favorite civilized hot springs are called "The Springs" near Idaho City. The combination of soothing music, large swimming pool, and cold drinks make the experience remarkable and unforgettable.
The Springs Resort
Wild hot springs can provide similar comforts and relaxation, but they could be a hit or miss. Since there are no reservations, they could be extremely busy, especially during weekends. Idaho's Trail Creek Hot Springs are an example of that. The terrain is often slippery because of algae: making it not ideal for children. Aside from all that, wild hot springs have the most amazing views. There are no time restrictions and essentially no rules (as long as the environment is respected and preserved).
Trail Creek Hot Springs during the Winter
Civilized hot springs are great if you want certain comforts and accommodations. Wild hot springs are great if you want to completely escape civilization and enjoy nature in its rawest form.
Trail Creek Hotsprings
Idaho's rapid growth has many locals frustrated with the well being of their state.