Different markets. Ubiquiti's software is no where near as polished as Meraki. Ubiquiti is working on a cloud controller function to reduce the barrier to entry for some of their products.
Their product lines are already based on cloud controllers, and despite some minor quirks (java, adobe flash…), the software is reasonably polished. But their main selling point are cost and hardware quality, their hardware is at the same time amazing and cheap, and the controller software is free. They sell like water around here.
Very recently I saw the deployment of a network with some 12 APs using Cisco hardware, estimated cost ~$20k (without the software licenses), and it ended up not working very well. The same setup would cost around $1500 with Ubiquiti, and zero software licenses.
I haven't seen the Meraki software, but what I have seen of the Ubiquiti software is excellent. The UniFi controller does in fact run in the cloud. Granted they could do more on the cloud front in terms of having something pre-built that you can activate with a click.
I'm not sure I'd want my wireless controller in the cloud though, I like the fact that the UniFi controller runs on anything from an 12 core x64 down to a single core ARM board depending on the size of your installation.
There's a significant difference between being able to run software "in the cloud" like how Ubiquiti instructs end-users to install Linux and then UniFi on EC2 and having the entire platform "in the cloud" and ready to use by the end-users with the operational cost rolled into the purchase price/support contract.
Requiring end-users to launch EC2 instances is missing the point of easy to deploy & maintain.
Ubiquiti is working on providing the controller "in the cloud" under the latter model. You can register and use their hosted system for mFi right now. Other stuff is coming.