Stellar actually consists of two entirely different code bases at this point. It started out as a fork of the ripple code base. That software, called stellard, is still running in production. However, about half a year after launching, Stellar subsequently released a completely unrelated payment system called stellar-core. Stellar core is based on a new consensus algorithm (called SCP), and an entirely new code base. Because it is a clean slate design, there is no backwards compatibility and any transition will presumably take the form of either a flag day or trading old stellars for new stellars while both networks run for a period.
Stellar-core has many differences from stellard (and hence ripple). One of the big differences is the new consensus algorithm, SCP, which was released with a proof of safety and boasts being "optimally safe" for a given configuration and failure pattern. SCP allows a lot of flexibility in terms of how nodes configure their quorums, and is explicitly designed to accommodate Byzantine failures (where bad nodes lie) and different nodes trusting different subsets of the system. By contrast, ripple uses a fixed 80% threshold, and their analysis does not apply to cases in which different nodes have different sets of nodes to trust. (If what ripple calls the unique node list, or UNL, is not the same everywhere, then safety proof does not apply.)
There are numerous other differences between the two systems at both the implementation and protocol level. For instance ripple allows freezing currency one has issued, which Stellar does not seem to support (at least yet). Stellar is explicitly inflationary, with 1% new coins being created every year and all fees being recycled, while ripple destroys fees, meaning the total number of ripples in existence is slowly diminishing over time. Stellar uses the Ed25519 signature scheme (basically Schnorr) and 32-byte public keys as addresses, while ripple uses ECDSA and 20-byte hashes as addresses. At the implementation level, stellar's protocol is specified using Sun XDR, whereas ripple uses a combination of google protobufs and hand-written marshaling code.