Factom stores data in a blockchain that's maintained by their network of federated servers. Tierion lets you create a verifiable record of any data or business process by anchoring your data to the blockchain. No altcoin required.
We've created an open standard called Chainpoint for anchoring data in the blockchain. Like Factom, we use Merkle trees and periodically insert a transaction containing a Merkle root in the Bitcoin blockchain. Unlike Factom, we give you a blockchain receipt that can be stored in your local database and shared with other systems. You stay in control of your data.
If you build an application on Factom, you're dependent on the Factom blockchain. If Factom fails, your application stops working. You have to continually acquire Factoids to write data to Factom. With Tierion, your data and your blockchain receipts can be stored anywhere - even in another decentralized datastore. There is no long-term dependency on Tierion.
I suspect that we'll see many approaches to anchoring data to the blockchain. Each approach will differ to accommodate various use cases. For example, Blockcypher has a free API call that allows you to store data in OP_Return, and Stampery has a product for notarizing documents in the blockchain.
Disclosure: I designed the Factom Explorer and played a key role in the launch of Factom.