Watch if I can, phone if not, and if the store's terminals support EMV (and I'll preferentially shop at stores that do for the kind of item I'm buying) I'll use my card. My city has a Target (supports EMV) and a Home Depot (EMV) for card purchases and for groceries I'll go to Dierbergs (NFC) and electronics I get from Micro Center (NFC). The local Apple Store supports purchasing through self-checkout and Apple ID/Pay, and I believe they also support NFC but I haven't tried it as I like to just grab my item, scan, pay on my phone, and leave.
I don't like swiping magstripes because they're totally unencrypted, so I avoid it where possible. For me Apple Pay and similar systems (Google Wallet, etc) are about security; I've had my card number stolen multiple times in the past and not only is it a hassle to clear up but it's a form of identity theft. I am not okay with my personal details being out there.
For Internet purchases I use one-time cards, which my bank deals with decently well. They can even handle premium ship purchases from World of Warships, which is outside the US and also uses a third-party processor for its sales. I didn't even trip a fraud alert with any of my ship buys (most recently on Monday), likely because I'd used a generated number which can only be done by someone with all the account credentials, including (in my case) 2FA. It's a shame that we can't yet use Apple Pay with Safari but I understand that's in the works. Hope it works with Warships.
Good to see that real transaction security is finally coming to the US to a point where I rarely need to use magstripe swiping anymore. And as for the accusation that EMV transactions are slow -- that's being worked on and should be much faster soon.