Apples and oranges.
On the surface, they both advertise themselves as language learning tools. It’s very easy to compare them at a glance and so people don’t always take the time to recognise what they offer and how they’re different.
Duolingo teaches users how to form sentences and grammar (to some extent at least). It does this by introducing vocabulary and then getting the user to make up sentences, find the missing word, etc. with this vocabulary to help better the user’s understanding. In my opinion it’s good for consolidation and practice, but not so great at teaching people new words and making sure that they retain that information. In short, it’s good at improving someone’s competency in a language and providing a good basis but it won’t get you to fluency.
Memrise has a heavy focus on memorising vocabulary (although the official courses seem to prefer getting you to try an memorise sentences which I think sort of misses the point). It isn’t very good at checking the user’s adeptness in forming sentences but it is very good at making sure you remember words. This means that it feels more useful as the user can see that they’re making progress as they remember more whereas Duolingo gives you the tools to speak a language well but you can’t tell because you don’t know enough vocab.
The thing is that they both say that they can teach you a language, and Memrise is better at living up to that promise. After all, you can get by if you know the words and don’t know how to exactly put them in a sentence but you can’t if you know how to form a sentence but don’t know the vocabulary to do it with.
Obviously, they’re very different products, each with their own strengths and weaknesses and I honestly believe that they do compliment each other in some way. A lot of people compare them because they’re looking for one service to get them fluent when really language learning is much more complicated and requires several approaches at times to be efficient. There is no perfect pasta sauce, only perfect pasta sauces. Each provides something different that the other cannot provide because it’d make everything needlessly complicated when these websites thrive off being simple and easy-to-use.