Okay, a couple of things -- I'm not an Implant user, but also am a sexual health counselor. I AM, however, a very long-time user of the IUD, so I'll talk a bit about that, too!
It is possible for your period to lighten or disappear with either the Implant or the hormonal (NOT the copper) IUD, though it is not guaranteed. Skipping your breakthrough bleed while on birth control is generally fine for your health. Of course, if your provider knows your body and makes any specific recommendation against it, I would take that into consideration -- but I would also seek a second opinion, just in case. Some doctors are out-of-date or pick up on the stigmatization of being sexually active and that can leak into their practice.
Insertion of the Implant can feel a bit less invasive than that of the IUD (the Implant is inserted into the arm using a syringe, while the IUD is inserted through the cervix). That being said, the hormonal IUD can last up to 7 years, and the Implant lasts only 3. So it's a matter of weighing those pros and cons, among others.
I like this quick article from Bedsider
on which medications might interfere with birth control. People on most medications can still take hormonal birth control, but may just want to consider their context when choosing a method (like your doctor's mention that the shot isn't a good option for you).
It sounds like you've already found our Birth Control Bingo: The Contraceptive Implant
article -- what other questions do you have?