You will probably get a variety of answers to which is better for a double chin. Each of the options you listed has pros and cons, so I will try to help explain the differences.
Kybella is an injectable product that is naturally found in the body and destroys fat. It involves a series of injections ranging from 2-4 treatments but up to 6. The actual treatment and number of vials depends on your anatomy. The heavier the neck the more treatments needed. As far as discomfort my patients really haven't complained of any. This is probably related to techniques used since I do perform all of the injections on my patients. The treatment takes about 5 minutes in the office with no down time. There is some swelling that takes place afterwards and treatments are spaced out every 6 weeks.
CoolSculpting involves a vacuum device and cold temperatures. The hand piece is more of a one size fits all so your anatomy really depends on whether this could be an option for you. For heavier necks it can help. If you have less fat, then it cannot pull the fat in and effectively treat. Depending on whether your provider has the newest device or the older model, your treatment will range from about 30 minutes (newer model) to an hour. Because it does involve suction this would tend to be a little more uncomfortable in my opinion, but there are no needles.
With both of these treatments the results are not immediate. As mentioned above, Kybella takes from 2-4 treatments spaced about 6 weeks apart. CoolSculpting usually involves two to three treatments but some do get the result they wanted with one. Neither of these will address significant lax skin and neither will give you a surgical result, which are important to realize before proceeding.
I'd recommend you consult with a facial plastic surgeon to go over all of the options for the double chin and find out which one works best for you.
I hope this helps and good luck.