OK. Here we go.
10mm, cos I compete and that is the maximum allowed. I train like I compete (to depth, not dropping the weight, touch chest, etc) so no point having a 13mm. So my choice is more to do with logic than function. That said, I don't see the point of a wider belt as it would get in the way with deep squats. 10mm is more than enough if you use it as intended (to force your mid section out and hold it, not to "save your back".)
So, no, I never wish I had a 13mm belt.
I use a Toro lever belt so zero break in time. You only need to break in a belt with prongs as they can be real difficult to do up and undo with a stiff new belt. The rest of the belt you want as stiff as reasonably possible to do the job.
Powerllifting belts are not suitable for Olympic lifting. Thats due to the much deeper squat they do with snatches. They need a thinner belt to avoid pinching against your ribs and hips. Also, being a raw lifter, they don't add anything to a bench press as your air is not being pushed into your gut, for bench it goes into your upper chest.
Also, I only use my belt for my heaviest work sets in three of the the big 4 (squat, deadlift, overhead press) as I don't find them necessary for accessories. You can if you wish, I just don't bother. It just kind of gets in the way and I look awesome and pretty without a belt, or a string singlet, douchebag baggy hat and skinny jeans.
I considered both a single prong and double prong belt because apparently to use anything else at elitefts made you ghay. But after trying on all types the lever belt was soooooo much easier to use, quicker and very secure. I don't frig around with "loose belt on warm ups, tight belt on max sets" so a lever is just fine. If I drop weight I can adjust the belt without too much bother, and vice versa.