I will give you a short review of each procedure and then compare the pros and cons of each.   The lap band is a restrictive weight loss procedure.  The band divides your stomach into two sections, a small top stomach and a larger lower section.  If you compare a hour glass to what the band does to your stomach, than you will have a better understanding of how it works.  Just like putting water in an hour glass allows the fluid to quickly empty from the smaller section into the lower larger section,  if you drink sweets they will quickly empty into the larger portion of your stomach and you will not feel full very long.  And if you eat a large piece of meat, and don't chew it well it will get stuck like rocks in an hour glass.  The band is adjustable so it can set for each patient at a different fill level.
The sleeve gastrectomy is also a restrictive procedure that makes your stomach into a tubular structure.  It also has the same problems as a band in that sweets go down easily and if you eat too large a piece of meat it may get stuck.

I believe that the sleeve does not offer much of an advantage over a band but has a significant increased risk of complications.  The main advantage of the sleeve is that there is not an implant.  But the procedure is permanent and if the sleeve stretches there is no way to adjust it.

In my practice I prefer banding over sleeve gastrectomy because I believe it offers an excellent chance for long term weight loss with the least risk.  As stated in other articles whether to have a bypass or a band depends on many patient factors.