Getting a new phone as part of a 'subsidised' contract is effectively borrowing money to buy a phone. Your loan repayments are the monthly fee. If you have the cash, buying the phone up-front is almost always cheaper.
BYOD means $20 off your monthly bill (or subsidizing is +$20, whichever way you look at it), and the BYOD rate is legitimately substantially cheaper than similar plans from AT&T or Verizon.
Plus even if you subsidize the device the terms are far better. The $20/month goes towards paying off a debt, which is simply unsubsidized price - subsidized price. If you leave early you pay the remaining balance and the phone's yours. This is in stark contrast to AT&T's rather punitive early-termination fees that exceed the actual subsidization provided initially.
It's absolutely cheaper to buy devices outright here.
Example of Three's One Plan for a 32GB 5s (£):
24 mo contract
Device 99
Plan 46
24 mo total = 1203
12 month contract + BYOD
Device 629
Plan 15
24 mo total = 989
Two options here, if you buy a phone on contract for say $200, then you can always sell it in a year, or even two, for around double of what you paid for it. Example, iPhone 5's are going for around $450 in my local market. I just paid $200 a year ago for it on contract. Some people hate contracts and say it's cheaper to not have data or what have you, but like I said this is just this particular scenario if you are on a plan.
Option B, you can buy a device for full price, ie $650 and wait the year or two and sell it for ~$450 but now you have a gap of $200, but you still own the device outright. Sometimes depending on what carrier, you can get an iPhone discount of $100 when not in your contract and that could bring it down to ~$550.
These examples exclude taxes and exclude some abnormalities with the pricing and buying markets such as unlocked > locked phones such as Verizon. Verizon phones don't have the same desire as AT&T phones because of the CDMA vs GSM difference with being able to use it on other prepaid carriers easily and worldwide use.
Anyway, that's my two sense from what I've learned over the years. If you buy a phone on contract and take care of it, you'll still get a great phone and double your money in a year when you go to sell it. That's how the markets have been treating them so far over the years.
Edit: I will say that if you wait too long such as the large jump from 4 to 5S, the resale value on the 4 is now dipped to ~150-200. So to me it makes more sense buying every release or two on contract, and then letting the phone pay for itself.