First glance at the pros and cons chart, the foam pads seem to have more benefit. Well, yeah, they kind of do, especially for the really ULers out there. Foam pads can serve as frames in frameless packs and they can be easier to pull out on the trail if you want a softer spot to sit on. Above all they're cheap and durable. However, (in my opinion) this isn't a fair trade for comfort. Comfort is very important for me as is a good night's rest on the trail, especially on multi-day treks.
Not everyone will agree with me, and other's criterion could be weighted slightly different than mine. So if you decide to go the foam pad route, at least get a closed cell (as opposed to open cell pad). In short, an open cell pad will absorb water, like a sponge. That's the last thing anyone would want. By using a closed cell pad you avoid that problem altogether.
My recomendation for a foam pad is the Thermarest Z-Lite.
I prefer airpads to foam pads, mainly because comfort is very important to me. Air pads do tend to be on the heavier side, but there are some fairly lightweight options out there. Aside from comfort, air pads are more packable which is a good thing. I, personally, don't like having equipmen outside of my pack - if I can help it. Typically, a foam pad will compress/roll down to a size smaller than a football. I personally prefer an air pad that is 2” thick or more, and if you are a side sleeper, you’ll likely find the same.
A nice lightweight option is the Thermarest NeoAir.
My favorite (and the one I currently use) is the Big Agnes Air Core mummy pad. It's a little heavier than the NeoAir, but it's cheaper and provides great insulation during the colder months.
Each hiker will have their own, personal, criterion for what is important to them. People taking a real minimalist approach will probably prefer a torso-length foam pad. People like myself, who value a good night's rest, will most likely go the air pad route. Everyone's personal criterion might not carry the same weight or importance, but it's vital that each hiker makes the best decision for themselves based on their wants and needs.