First of all, Depo-Provera is an injection while Implanon (Nexplanon) is a rod that is implanted into your arm. They both issue a dose of the hormone progestin which stops a woman's ovaries from releasing eggs.
Depo-Provera usually stops a period for the entire time it is being used (up to three months) while the implant stays in place for three years and releases progesterone treatment to thicken the mucus of the cervix which keeps sperm from joining with an egg.
The main advantages of Nexplanon are that you don't have to take it regularly as it lasts for three years and fertility returns soon after the implant is removed. These contraceptives have a higher up front cost than a lot of other methods of birth control.
The main advantages of the Depo-Provera shot is that it is an affordable and highly effective form of birth control. Lots of women don't see their periods while on the Depo shot while implant users are prone to spotting and irregular bleeding.
Check out WebMD to go through the side effects and other features of the Depo-Provera injection and Nexplanon: http://www.webmd.com/sex/birth-control/.....