So, a few things to consider with this questions.
1. Yearly Upgrades. As mentioned above, do you want the latest iPhone every year. This is the biggest reason to do the Apple Upgrade Program. You get a new iPhone every year, and that's pretty sweet. Some carriers offer yearly upgrades, but get the fine details. Some carriers say you can get a new phone every year when there is fine print. "Yes you can get a new phone every year if you pay 70% of the current phone off". Several carriers make you pay much more than 50% of the phone before you can upgrade and can get away with saying you can upgrade every year as its technically true. AUP only makes you pay 50%.
2. Cost of Month to Month vs. Contract. Depending on your carriers pricing, Month to Month could be much cheaper than doing a contract. The reason being that most carriers make you pay $40 per phone in contract. That's the subsidized price of the iPhone, $199 to $499 plus $40 a month. Now, when you go month to month your no longer pay the subsidy fee. Depending on your carrier and the plan your on can mean a $15 to $25 dollar discount on that $40 line fee.
No putting that into play. If you save $15 a month over the course of 24 months that's $360. If you were getting the 16GB 6s that retails for $649 you really only paid $289 for the phone after your discount (649 - 360 = 289). So you didn't save anything and actually paid $90 more for that iPhone. But if your on a plan like I am where I'm saving $25 a month, that's a savings of $600. So even getting the 128GB 6s+ that retails for $949, with those savings I really only paid $349 instead of the $499 I would have paid in contract (949 - 600 = 349). So I saved $149.
3. AppleCare+. AppleCare+ could be one of the reasons you may or may not pick the AUP. The AppleCare+ plan is not free. Your paying for it on top of that price in reason 2. The prices in reason 2 are just month to month prices of the iPhone and did not take in to account the AppleCare+. If you get AppleCare+ every time you upgrade, as I do. Then you are saving that $149 in the last example. However, If you never buy AppleCare+, the you paid an additional $129 for something you did not want. So, in my last example with $25 a month off you still save, but its lowed to $29 if you didn't want the AppleCare+.
Also, Your carrier may offer a warranty that may be somewhat better than AppleCare+. The reason that is, is Loss prevention. Doing the AUP your always paying a phone off. Its really not any different than if you did a carriers payment plan or contact in the sense of you don't ever really own the phone and even with a contact most people get a new one as soon as that becomes an option. But if you loose your phone on any of these, your kind of S.O.L. Plans with carriers may offer warranties that while more expensive in the long run than AppleCare+, includes loss prevention that would make it less painful to replace a missing phone.
If you don't want AppleCare+ and the savings of month to month didn't actually save you anything with the plan your on. Doing your carriers plan may be a better option.
4. Freedom. With the AUP your not tied to your carrier. They can't hold the "We own you" above your head when your calling to complain about their bad service, and you can leave them at anytime. Most people will probably never switch carriers, but for those that have issues with their current carrier. This is a huge selling point.
5. Apple. You get to say in the Apple ecosystem. For the die hard Apple fans out there, this really is the only option.
In closing. Review this information closely. Ask your carrier these questions without letting them know your thinking of doing the AUP so they don't try to rope you into something. I hope this helps you make an informed decision.