I just bought a Neoair (Thermarest) (got the idea from Staehpj1). I used the 20% off coupon REI sends out this time of year for their anniversary. No experience or review yet but I'm looking forward to the comfort and small packing size. I bought it for my wife to use backpacking together, and for me to use solo bike-touring.
In the past, I favored closed-cell foam. Currently using a Nemo Z-fold short model. Past pads, I cut off below the knees to save weight and bulk. R-value for these pads are about 2. They work, but comfort is not great. The main reason I've stuck with them is durability. I wanted my stuff to be bomb-proof, especially when I bring my 90-pound dog (not on the bike, but all other trips).
I also have the self-inflating Thermarest. R-value on these is 5 and mine are the 25"-wide version. I've had four for the last 15 years and only had to make one repair. I used them with the dog too, but not backpacking -- they're too big and bulky. So they're used for car camping. I will also use them on top of the cots when camping for longer durations -- that outfit requires the full-size truck or a utility trailer. I wouldn't take one bike touring because when they're rolled up, they make a awkward long package. The Neoair isn't full of foam so it can be folded and rolled into a much smaller package that will fit neatly in a pannier.
I'm actually hoping to use a hammock for my next bike tour. I have and have used hammocks with success. I find them harder to use for a group, but for solo camping they can work great. It's always a challenge to find an ideal place to hang it, especially when one end can't be hung on a motor vehicle which makes a convenient and sturdy anchor. Safest bet would be to take a hammock and the Neoair as a backup in case I end up without a place to hang the hammock, but that offends my minimalist sensibility. It would be better to leave the hammock because the pad can always be made to work. So I will have strengthen my resolve to find places to hang the hammock and dare to go without the pad. Some destinations are better than others for this, and what I have in mind for my next several tours should not be too daring, but I can see how it might affect my itinerary. I might be reluctant to pass a good hang spot and keep pedaling into later hours if I'm worried I won't find another. I might also find myself with the hour getting late and needing to pedal-on because there's no where to hang. I tend to plan my routes carefully, but not my pace or timeline.