Both physicians can remove moles, as can other types of physicians. However, Dermatologists remove many more moles than Plastic Surgeons and therefore, are typically the most experienced "mole removal" physicians.
Dermatologists are better trained in identifying the type of "mole" (or skin cancer) that you may have and hence, selecting the most appropriate and least likely to scar removal method. The choice of removal method is very significant in determining the final scar, if any. Dermatologists usually have a wider range of mole removal tools also. Often, what a patient perceives as a "mole" is something different than a mole that does not need to be excised, but may be better treated by light electrosurgery without any scarring. Or other times, the "mole" or lesion is not a growth at all, but a focal (single) inflammatory lesion (a very small single skin rash) that may respond scar-lessly to a topical cream. A "mole" may be a skin cancer and require an altogether different work-up and treatment.
Moderm Dermatologistic Surgeons are equally adept at suturing and reconstruction of wounds created from skin cancer or mole removal as Plastic Surgeons. Individual variances exist of course in both specialities. And some might argue that Dermatologists are better since they tend to perform these functions more than Plastic Surgeons as a general rule.
In summation, you should always see your board certified Dermatologist first for any "mole" or skin issue and discussion of who should remove it should start there after an accurate dermatologic evaluation.