Disclaimer: I designed the Factom Explorer and played a significant role in the launch of Factom.
That's a big question. Here are a few points:
1) Tierion does not require an altcoin. Factom does.
2) Tierion is a working product with paying customers. Factom is still in the very early stages of development. There is no user interface and only rudimentary developer tools.
3) You can sign up for Tierion in 30 seconds. We have an easy to use API and developer documentation. With Factom, you have to install three command line interface programs, exchange Bitcoin for Factoids, convert Factoids to Entry Credits, and then you can use the command line interface to write data to Factom. It's a very complicated experience. They are working on a docker image to make things simpler.
Factom has chosen to create a blockchain that is anchored to the bitcoin blockchain. If you choose to use Factom, your application will have a dependency on the Factom blockchain. If it fails, your application will probably fail. They have also chosen to create an altcoin. If you choose to use Factom, you will always need to acquire Factoids to write additional data to a Factom chain.
With Tierion, we've created a scalable protocol for recording data in the bitcoin blockchain and generating blockchain receipts. These receipts are portable. You can store them wherever you like. You can also share them with other applications that can independently verify the receipt.
Factom is still in the very early stages of development. They just reached their first milestone required to receive their first payment from the Factoid crowdsale. The second milestone requires Factom to build a storefront and a consensus mechanism for eight federated servers. This will likely take several months. The third milestone requires moving away from the current centralized model to a decentralized model. This will likely take several additional months.
I hope anyone who has been looking at Factom gives Tierion a try. I think you'll prefer our developer experience and you won't miss the reliance on an altcoin.