To begin, these services are not the same however, that is not what I am comparing. The true comparison is between their streaming services; Sound Cloud Go and Mixcloud Select. I will omit the company name for this and refer to them as Go and Select.
The major difference between the two services, as well as the one I expect to be most prevalent, is money. To those of you who are not content creators on either of these sites, I will give a short synopsis of how people earn money on each. For Sound Cloud, creators can upload anything they want that is original works. Bootlegs and DJ mixes are not allowed. As for payouts to creators, while you may expect that the audio ad revenue goes to the creator, you would be wrong. Beyond that both services are similar with their paid features. Mixcloud has just began rolling out Select. Mixcloud is a platform for DJ mixes only, Select allows people to subscribe to your channel of mixes for a price the creator sets, and the creator receives an amount of that.
In the end, it is too early to say who will win however, my personal focus will be on Select because it distributes a portion of the revenue to the creator without the creator having to pay Mixcloud to hold their work.