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