I use both, and have used both for about 1 or 2 years. This answer is based on experience I have with both providers. You're asking this on a bunq site though, therefore answers might be biased here ^^.
I prefer bunq, and in fact, I've switched to bunq from N26.
When using N26 I had quite some complaints:
- the app sometimes didn't work, and frankly I feel their UI isn't well polished in all places.
- payments in foreign countries were troublesome for me, and I wasn't always able to fix things through the app on location leaving me with no payment option.
- I've had a bad experience with their customer support, where they were essentially not able to help me with a banking problem, and support did take quite while to respond anyhow.
- installing N26 on a new phone, if the old phone is dead, is troublesome. This is done using a few recovery steps, of which some steps don't properly work (for example, entering an SMS verification code) requiring you to do this process 3 to 5 times.
- you wouldn't get an maestro card, just mastercard (although that's fixed now).
- various other minor issues I won't get into now.
Although I love the fact that they provide the service for free, I didn't feel confident in them due to the thighs described above. I didn't feel I was able to trust them as my _main_ banking solution.
In the end I decided to switch to bunq, and was happily surprised by the features provided in their premium package. I like these features, I feel like everything is much more polished, my support interaction was awesome with instant responses and solutions, and things like API access is something amazing for me as a developer. I feel much more confident using bunq, which is important for a service that you use daily, and manages your money.
Such good service may cost something, I think. Although €8 is quite a bit more than the competition, I believe it's worth it.
So, if you're really searching for a free service, give both a try (N26 will offer more for free). If you're willing to pay for the service, stick with bunq.
I've yet to experience similar problems with bunq as I did with N26. Go bunq!