There are several major differences. Bitcoin is a currency with a built in payment system for its currency. Ripple is a payment system for arbitrary currencies with support for cross-currency transactions.
One big difference is that currencies in Ripple are represented as debts (IOUs). This is much the way currencies are represented in the conventional banking system. When you say, "I have $5,000 in my bank account", what you mean is that the bank owes you $5,000. When you write someone a check, you are transferring debt so that their bank owes them more money and thus they consider you to have paid them. Ripple works this same way -- payments occur by a transfer of debt (IOU).
You can generally get a Bitcoin transaction through for free if you're patient. Ripple transactions always have an XRP cost. In practice, this cost should remain very low. Transaction fees are destroyed in Ripple, they aren't paid to anyone.
Ripple payments can incur fees other than transaction fees. It is hoped that competition will keep these costs low. If your payment requires using someone else's liquidity, they can impose a fee for that liquidity. IOU issuers can impose fees on transfers of IOUs.
Ripple transactions should confirm more quickly, typically in under 15 seconds.
While Ripple is designed to operate without a central authority, currently all servers are operated or managed by Opencoin and the server code has not been publicly released yet. So it's not really open source or distributed yet, but it will be. Currently, most XRP (the units used to pay transaction fees) are held by Opencoin. Opencoin plans to begin giving them away shortly.
It is also important to understand that using Ripple as a store of value for fiat currencies imposes a counter-party risk. If you hold dollars in Ripple, someone you have chosen to trust owes you those dollars. If you misplace trust, you can wind up with uncollectable IOUs.
Ripple uses gateways, companies that make it their business to make "settle on demand" agreements with people, to hold IOUs. Ripple is much less useful for payments of fiat currencies if there aren't reliable gateways you can trust to hold your money.
In function, Ripple is more like PayPal or Visa than Bitcoin. But its internal implementation is based on the same technologies Bitcoin uses -- public transactions, no central authorities, cryptographically secured transactions, peer-to-peer transaction propagation, and so on.