Replace-by-Fee vs Child-pays-for-Parent? Both RBF and CPFP attempt to solve the problem of transactions not confirming because of an insufficient fee. What are the pros/cons of using one vs the other?

Are both currently functional and available for use on the bitcoin network?
Replace-by-fee means transactions spending the same coin to the same addresses are not considered double-spends by the network and are still relayed, as long as they pay a higher fee than the preceding transaction.

Example:
Alice pays Bob with a coin worth 1 BTC, sending 0.5 BTC to Bob, 0.49995 BTC to herself as change, and 0.00005 BTC to fees. Alice sees that her transaction is quite slow to confirm, so she sends an identical transaction (spending the same coin), but with twice the fee. The network relays the updated transaction and rational miners quickly mine the higher fee transaction.

Child pays for parent means, as the name implies, that spending an unconfirmed transaction will cause miners to consider confirming the parent transaction in order to get the fees from the child transaction included in the same block.

Example: Eve spends 1 BTC at a shop owned by Alice. But Eve is greedy: she only pays the bare minimum fee, and her transaction will take hours to confirm. Alice spends Eve's transaction to her banker Bob, but this time with a higher fee. Miners will now want to confirm Eve's cheap transaction in order to be able to include Alice's more rewarding transaction in their block.

RBF is currently live since 0.12, but is opt-in for the spender: Unless the spender marks the transaction as replaceable with a non-maximal sequence number, the transaction is final.

CPFP is not a change in the protocol, but in miner strategy.
Since it is rational for miners to implement it (they make more money), it is expected that most miners do implement it. At least Eligius seems to have implemented it. As mentioned by Pieter in the comments, any miner using version 0.13 or above will mine using CPFP rules.

Which one should you use?

If you're the spender and want your transaction to confirm faster, use RBF. If you received a payment and are unable to convince the sender to up the fee, or the transaction is marked as non-replaceable, use CPFP.

Better yet, send your transaction with the proper fee the first time.