Is Invisalign Better Than Braces?

I will guarantee you that braces are a better treatment choice than Invisalign. I can also guarantee you that treating with traditional braces will take less time and your results will be superior. The only way to move a tooth in 3-planes of space is to physically attach an appliance to that tooth in order to accomplish those objectives.
Invisalign is a plastic cover that fits around a tooth with no physical attachments to the tooth. Invisalign, if not worn 23 1/2 hours a day, will not work. I found that most of the cases that I have treated most adults fall short of this and as a result, our treatment objectives are never met.
I do not have your records, but if your orthodontist has told you that your case is going to take three years, then there are also some bite issues. It is very difficult to align the bite with Invisalign. Most of the Invisalign being performed is by dentists who are not trained orthodontists. If straightening teeth was only about alleviating minor misalignment, there really would be no need for orthodontist.
Orthodontics involves so much more than just straightening teeth. In most of the case, I see there are bite issues and this requires specific diagnosis and treatment for each individual case. Believe it or not, we want you to have a beautiful smile, but teeth are for eating with and proper alignment is our main objective.
Traditional braces is the best way to accomplish this. I know your main concerns is aesthetic while going through treatment, and if that is so, look at braces which are placed behind the teeth. This is called lingual orthodontics and 3M Unitek with IBraces has the solution. I have been doing linguals for about two years now and the results are amazing. I have completely stopped Invisalign in my practice and utilize this method now.

Invisalign is not necessarily "better" than braces just as braces are not necessarily "better" than Invisalign. The "best" option is determined by informed consent and an honest dialog between you and your doctor. This can be done by telling the doctor your treatment goals and your doctor then explaining the different options available to achieve those goals along with the advantages and limitations of each option, In this way you can make an informed decision on the "best" option for you.
If your goals are to achieve as close to "perfection" as possible in terms bite, overbite, and teeth straightening correction, then traditional braces may provide you the best option. Braces will generally give you a better "technical" result. By "technical" result, I mean the difference in correction that a dentist and orthodontist sees and that seen by the untrained eye or layperson. In other words, there may be no additional benefit to you by going with with the "perfection" option.
Keep in mind that working with Invislign is an aquired skilled that is gained through experience. There is no Invisalign school. The training that Invisalign provides doctors is limited. Therefore, your provider's recommendation to you will be somewhat tempered by his or her experience with Invisalign.
In your case, specifically, it may be accurate what you were told. It could take up to 3 years to correct your bite etc, if your orthodontist's goal was an "ideal" or close to "perfection" result. That, however, may not be your goal. If your bite is comfortable without problems and Invisalign can achieve your goals...then maybe the choice is easier than you think.