I wouldn’t say there’s any particular thing that Starling does better, and any features they currently have that Monzo don’t, I’m sure Monzo will get pretty soon (and vice versa). In terms of the raw product, I see very little difference - they’re both early products, but both great.
It’s more just that I find myself disliking some of the directions Monzo is heading in. They come across more as a startup that happens to be in banking, with all the haphazardness that tech startups bring, where as Starling seems to be more a new bank that is using modern technology. Sure, they’re both early stage, but Starling just seems more considered. Some of Monzo’s moves, like crowdsourcing strategic decisions, constant overdraft pricing and ads in the feed have left a bad taste in my mouth. Maybe it’s just my perception, but they seem to be guided more by a desire to be different than a desire to make the best choice.
Maybe Monzo’s strategy is better - I can certainly see the argument that you’re not going to win customers by being a normal bank with better tech and customer service, and that you need to be starkly different to make inroads. Personally, though, I think I prefer Starling’s approach.
Edit: I don’t want to get into a flame war about whose favourite bank is better. There are some things that Monzo does better, and if they’re important to you, good for you. I’m glad both exist.