To better understand what Web UI is, compare Geth and Mist. The first has all the functionality one requires in order to work with smart contracts. The second has limited, compared to Geth, functionality, still, we use it more often than we use Geth. The reason is obvious: Geth provides raw command line functionality, while Mist has it nicely wrapped.
However, Mist's "nice wrapping" is limited, as it just lists functions in a long list. Using your Browser functionality we can do better: for a particular contract we can create a perfect web page with all bells and whistles of the modern HTML 5.
Note: When providing the Web UI to the customer, you should always keep in mind that this is a new area, and some people do not know how to set up the environment for it to run. So do not forget to explain (in an error message perhaps) to the client that a Geth should be running in order for the browser to "see" the block chain.
It is also important to keep in mind the security considerations: to access funds, your customer should enter the password to the wallet, and if it is done through Web UI, it means entering a password in the total stranger's (yours) Web page. Look how it is handled in my HTML.