I used Apple Pay on London Transport, and it worked well. One benefit that you have visual confirmation from your phone that you have tapped in - the phone vibrates and "beeps", and you get a message confirming that you've used Apple Pay at xx:xx in "London", which does give some at least some reassurance that you've not tailgated someone through the barrier by mistake. I also felt safer using the phone than my bank card - I'm probably going to take my iPhone out of my pocket on the tube at some point anyway, whereas I'd otherwise never take my bank card out and wave it around for the world to see! Also, I'm far more likely to notice someone stealing my iPhone than my bank card purely because it's more bulky.
The risk, of course, is battery life. As has been said, it's at your own risk, and it is your responsibility to ensure that the device is charged. However, you are upgrading to an iPhone 6S and should see a noticeable improvement in battery life. Since I've upgraded from a 5 to a 6, I've never had any issues with battery life that wasn't my own fault (failing to put it on charge - D'Oh!).
If you think it's possible/likely that you will not have enough battery, I'd stick to a CPC over the iPhone. But I used my iPhone on two consecutive days with moderate usage and didn't encounter any difficulties. If your battery is draining quicker than you think, and you're on a bus, you can turn the phone onto airplane mode to conserve battery power if you need to. Apple Pay does not require your phone to have an internet connection. Of course, you'll be sacrificing your ability to use the phone's data and telephony services which is probably a concern for you, but it's better than being fined for an incomplete journey, and besides you won't get much in the way of data when you're on the tube!
A hint if you are going to use an iPhone on TfL - you can and should "prime" the phone using your fingerprint prior to getting to the ticket gate. It only saves a few seconds, but that few seconds can slow things down quite a bit in the rush hour.
Give it a shot when you get your new phone - you may find it works well for your needs, you might not. I've found Apple Pay is very easy to use on the whole - I've used it on TfL, but also regularly use it up here and it works very well. The few times I've had issues, it has been the retailer refusing to acknowledge that they accept it, and unfortunately in these scenarios you're the one who looks like an idiot!
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If your original card isn't contactless, maybe? There's also the point that an iPhone snatched at the gates can be tracked by GPS and can't be used to make purchases until they've lifted your fingerprint, while a snatched contactless card can be used without verification to quickly empty your account with £30-or-less purchases.
An iPhone can also be completely disabled using the "Find your iPhone" service, rendering it useless to a thief. I'd urge all people with iPhones to make use of this service if you haven't set it up already.
