First, the phones have always cost roughly the same amount, the carriers simply beefed up their calling plans to cover the subsidy they were giving on the device up front. If you're losing updates soon, are you on the 4 or 4S? That phone probably cost $600-700, but the carriers would have discounted and you probably bought for $200 with the other $400 roughly baked into your contract, probably adding roughly $20/month. You can certainly shop around, but your new iPhone will cost about the same whether you buy from Amazon, Apple, a carrier, Best Buy or whatever. If you're looking to save, look at buying a 6. It's one model older, but still has almost all the functionality of the 6s minus the 3D Touch/Force Touch.
But yes, unless you take a carrier subsidy, you're no longer going to be under a contract. If you use a carrier finance plan, you're sort of under a contract, but the carrier would be taking the up-front cost of the phone and spreading it directly across a defined period. You can still leave whenever you want, but instead of a "termination" fee, you'd just have to pay off what's left on the phone.
Also, think of it this way -- if you're still on a 4 or 4S, you've probably been paying your carrier that extra $20/month to cover the subsidy well beyond when you stopped upgrading your device. Now, even if you do the carrier finance plan, you'll take the price of the phone and divide it into payments with your carrier. Once you've made those payments, then your bill will drop by that finance amount because you'll own the phone outright.
