Styling maps is just an added feature. Their main uvp is simply "maps". Competitor and alternative to Google Maps, Mapquest, etc.
Both Cloudmade and MapBox use OpenStreetMap data. Leaflet ( http://leafletjs.com/ ) was created by Cloudmade and is the JavaScript lib for putting tiled maps on the web. Mapbox have their own version of Leaflet, but it's essentially much the same if all you want to do it drop pins, work with layers, choose a tile set.
Both are comparable, and both are strong in the same space: Custom styled, tiled maps. And both are weak in the same place: routing.
Not to say that they don't do routing, but it's certainly not their forte.
Thankfully the majority use-case for most sites and applications using maps is simply "show a map, drop a few pins here and there". So having this map look and feel like the site is actually a good selling point.
Only allowed me to pick car as a mode of transport, and unrealistically suggested I could get across 14KM of central London in 14 mins, but ignoring those things this is very nice.
Would love to see the path output of this added to Leaflet and a standard form of API emerge for Mapbox, Cloudmade, Google Maps, etc.
Also Public Transport route and connectivity information is frequently a bit patchy in OSM, but this is steadily improving.
Email in my profile... that is, if you think we're your market.
Adding public transport, cycling etc. would be fantastic.