Factom stores data in a blockchain that's maintained by their network of federated servers. Tierion is an engine for 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 Factom's servers. If Factom fails, your application stops working. You have to continually acquire Factoids to write data to Factom. Or, you have to buy entry credits from middleman. 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. While Factom has plans to someday be decentralized, it's still a long way off from reaching that goal.
Another significant difference is ease of use. It takes minutes to get started with Tierion's API. Try this test. Sign up for Tierion and write "Hello World" into a datastore. It will likely take you less than five minutes. Now try writing "Hello World" to Factom. It will likely take you hours. You have to start by downloading and installing four pieces of software: Factom Wallet, Factom Wallet GUI, Factom-CLI, and Factomd. Next you have to acquire Factoids. Currently, the best way to do this is to buy some Bitcoin, open an account on Poloniex, and trade you Bitcoin for Factoids. Next you have to transfer your Factoids from Poloniex to your Factom Wallet. Then you have to convert your Factoids to Entry Credits. Next you have wait while your computer downloads the Factom blockchain to your local computer. It goes on and on... View Factom's install guide here.
Additionally, we connect with over 500+ software applications. This makes it easy to automate business processes and share data between the apps that drive your business.
I'd like to add, that both companies are very early in our product cycles. We have a few things coming that we're not ready to share. I suspect the same is true of Factom.
As Paul indicated, I provided design and technical input into Factom. Although we're competitors in business, we're also friends as evidenced by this epic selfie: (I'm on the left)