Easier to Build On
I think the key to Storj model is abstraction. Storj is designed in a modular way, so you can upgrade, swap out, and change features as needed. As you said making one UI would be a nightmare. Instead we provide an API for which the web interface rests on top. So if you want to change the base UI for a different use case or language go right ahead. Just make your changes to the HTML/CSS/etc. and you don't have to touch any of the core code.

In this case Storj make it easy to build "very specialized and easy to use" apps. If you want to develop a storage app would you rather use a C++ API or a nice REST API? In one case, you have to do a ton of work, in the other you are just doing a reskin to fit a different use case. After our tech is a little more solid I think I might write something like a 'Making a Storj app in 15 minutes' just to make the point.

Useful for the Average Consumer
So if you picked a random person of the street, sat them down in front of a computer, and asked them to store a file on a decentralized network how do you think that would go. Would the average user (who probably knows nothing about Bitcoin) be able to get some specialized token? Not to mention they have to probably download and sync specialized software.

Not so with Storj. The user goes to something like storj.io, pays for some bandwidth with their credit card(bitcoin or storjcoin), and begins uploading files. To use it they don't have to install any specialized software(although we will have that later for convenience), or go through the hoops of trying to acquire tokens. At the end of the day it just looks like we are offering a file storage service, so we can accept payments through more "traditional" methods. This opens up Storj to the entire market immediately, rather than just the Bitcoin market.

So its 5 minutes, vs. Signing up for Coinbase, verifying your account, waiting 3-5 days, buying x token on an exchange, using the app.

Protection from Price Changes
These other tokens are traded on open markets. That means they have a fluctuating trade value. So 100 GB might cost $5 one day and $10 the next. People might not like this so much, but if your stuck using one storage network and one token your going to have to deal with it. So lets say the speculative price of an external service shoots up to an unreasonable amount(data based cryptocurrency bubble of 2014 perhaps), the Storj network can store the files on its own network. If after a few days the price goes back down to reasonable levels. Storj can then transfer the files to the external network. So the cost of data storage on Storj will always be the lowest, because Storj does not have to rely on its own data storage network.

First to Market
Our development process is completely different. We want to release features and applications early and often. We want to build toward a solution than promising the moon and delivering months later. Our web nodes are working now, we are just adding polish and features.

Value in Storjcoin
Storjcoin provides more than just speculative value. Storjcoins are spent via tx fees to send network wide information. In our prototypes these will be returned to miners, but as the coin tech for it appears I might want to return these as dividends to the coin holders. So by holding Storjcoin you gain value from the physical storage and all the apps built off the entire network. So if someone pays in Bitcoin for their storage, Storjcoin will still have to be spent to send that information to the network. In that way Storjcoins will always build value either directly or indirectly.

So the value added: is easy to build on, immediately useful for average consumer, protection from price changes, first to market, and network wide rewards. There are a few more, but have I answered your question? I can move on to compute next, but I wanted to make sure I addressed the first part.