With liposuction, the amount of fat removed is measured and easily controlled in the right hands. Mesotherapy involves the injection of nonstandardized chemical that are meant to "dissolve" fat.
I have several patients who present to me for liposuction who have tried mesotherapy and report no improvement, or even a few who state that treated areas increased in size. In fairness, those patients with excellent results wouldn't present to my office for liposuction. I get the sense there are not many patients satisfied with the results, however.
If mesotherapy did actually work, there is another issue to consider in my opinion. Where does the fat, lipid, and cholesterol go? Hopefully we don't find in the future that it leads to premature vascular disease or heart disease.