Are there still any advantages to using an Oyster card for travel in London?

You can link up your railcard(cetain type only) and oyster card to get extra 1/3 off for off-peak trip. Contactless payment cannot do so

You can buy and use Oyster cards without registering them, so they allow you to travel anonymously, i.e., without giving a corporation the (immediate) ability to link your motion profile with your identity. (Of course, other factors might make it possible to predict your identity with some accuracy anyway.)

I don’t understand the point of using your credit card instead of an Oyster card. You’re just introducing more weight on the card and more reasons to lose it. I top my Oyster up with £20 and that lasts me a week+, no worries getting my debit card in and out all the time.
The argument that it’s faster to use your debit card is naught. If you walk up the elevators once a fortnight, you will essentially be cutting the amount of time it takes to top up for that period.

This might be because I don’t care about having an extra card in my wallet (hey, they can hold tens of them).

Not to mention, railcards make HUGE discounts on off-peak travel (which I still do a lot, even though I work full time). This doesn’t just apply to a select amount of consumers either, pretty much anyone can.

I firmly disagree that paying with ‘contactless’ cards is any better than an oyster card.

There are a number of discounts that are only available on Oyster – you can get these discounts loaded up on an Oyster card and they are then automatically applied at the ticket gate, but this can’t be done for contactless cards.

For a regular commuter, most importantly there’s also the Annual Gold Card discount. You get this for having any annual season ticket within the Annual Gold Card area. So for example if you live outside the Oyster zones you might buy a season ticket to London Terminals and then pay for your onward TfL travel with Oyster.

You won’t get any discount in the morning peak, but if you work outside Zone 1 then you’ll get one in the evening peak because you’ll be travelling from outside Zone 1 to your Zone 1 terminal station and so it’ll count as an off-peak journey, and you’ll definitely get an discount at off-peak times e.g. if travelling at weekends.

You still need to work out whether it’s better for your particular journey to buy a separate rail-only season ticket or to include a travelcard in your season ticket – this will vary depending on your exact circumstances.

One of the issues that could be encountered when using Apple Pay or Google Wallet for your contactless travel is when your device runs out of battery after you’ve started a journey – you will not be able to “tap out” and then will be charged the full penalty fare.

Most devices with contactless payment are still relatively new, but we all know that with time, our trusty phone batteries last shorter and shorter. If you forget to charge your device at work and get an important call on the overland on the way home that you just have to take, you might have some trouble at the end of your journey.

Weekly travelcard: Contactless weekly travelcard is only from Monday to Sunday, so if you arrive and leave mid-week, you might get better rates if you still get an Oyster card, and buy a weekly travelcard on that.

On the other hand it might still be cheaper if you don’t intend to travel every day for 7 days to just use your Contactless and use the daily capping rates. Also, if you start your journey after 9:30 every day inside zones 4-6, and do this at least twice in a week then you’re eligible for the (not really advertised) reduced off-peak day rate, which you get as a refund. Getting this refund to an Oyster card as a visitor is usually not possible, as you have to get back to the UK and touch in, but for contactless they can simply just refund to your card, even when you’re long gone.

Boat services: There used to be a difference between Oyster and Card fares on the Boat services as only Oyster was accepted for discounted fares, but as of 2017 both Oyster and Contactless users can get the discounted fare.

Buses and trams: There used to be some slight differences on some heritage bus services where Contactless was not available and there were some bus/tram connections in South London where the Oyster price was slightly cheaper than the Contactless one. As of 2017 these differences have been abolished by the new Bus Hopper fare.

Banking costs: See @JoErNanO’s answer about potential foreign banking costs associated with Contactless cards

Transaction Fees for Foreign Cards

If your bank charges you a fee, as well as a percentage, for every transaction you make in a foreign currency, you could save quite a bit by topping up an oyster card once every so often as opposed to using a contactless payment card every day. For example my bank charges me 3€ + 2% for each non Euro transaction. This would mean paying an extra 3€ for every day that I use TfL services (you are charged at the end of the day when using contactless cards). In my case I’d rather have an oyster card and pay those fees just sporadically.

Visa’s Might not Work

Last time I went to London I tried using my two French bank cards. As it turns out neither of then work because they’re Visa, and TfL’s contactless payment system doesn’t quite support them. MasterCard’s on the other hand should work seamlessly. Therefore here’s another advantage to using Oyster cards: no need to worry about incompatible contactless cards. Quoting from the linked TfL webpage on foreign cards:

VISA

Some Visa and V PAY contactless payment cards from countries issued outside the UK are not accepted for contactless travel. Visa expects all its contactless payment cards to be accepted soon.

If you travel in London regularly, we suggest you contact your issuer and ask for a new contactless payment card (newer cards have the latest technology and should be accepted).

You Can’t Lend your Contactless Card

Also, as noted by Gayot whose comment I shamelessly stole, you can always lend your anonymous oyster card to someone else (this is allowed as per tfl terms and conditions). You can’t really do that with your payment card.