There are several major differences. Bitcoin is a currency with a built in payment system for its currency. The XRP Ledger is a payment system for arbitrary currencies with support for cross-currency transactions.
One big difference is that currencies (other than XRP) are represented as debts (IOUs) on the ledger. 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. XRP Ledger transactions always have an XRP cost. In practice, this cost should remain very low. Transaction fees are destroyed on the XRP Ledger, they aren't paid to anyone.
XRP Ledger payments that use assets other than XRP 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.
XRP Ledger transactions should confirm more quickly, typically in under 10 seconds.
While the XRP Ledger is designed to operate without a central authority, currently almost all validating servers are operated or managed by Ripple Labs. So it's not fully distributed yet in that sense, but it will be. Currently, most XRP (the units used to pay transaction fees) are held by Ripple Labs.
It is also important to understand that using the XRP Ledger as a store of value for fiat currencies imposes a counter-party risk. If you hold dollars on the ledger, someone you have chosen to trust owes you those dollars. If you misplace trust, you can wind up with uncollectable IOUs.
The ledger can uss gateways, companies that make it their business to make "settle on demand" agreements with people, to hold IOUs. The ledger is much less useful for payments of fiat currencies if there aren't reliable gateways you can trust to hold your money.
In function, the XRP Ledger's way of handling assets other than XRP 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. One key difference is that people who choose to use assets issued by different counterparties can seamlessly exchange value with each other through a distributed exchange. So there's a huge interoperability benefit.