This question doesn't make sense -- Paxos and the blockchain solve different problems. You were probably misled by people talking about how the blockchain solves distributed consensus. That's a decent analogy but not a precise statement about computer science.
There are several differences, but the main one is that with Paxos all the members are trusted, and have to be under a single administrative domain. With the blockchain, the whole point is to come to consensus without trust in a central authority.
Other differences:
- Paxos (Chubby, etcd) and related algorithms (Zab/Zookeeper) are used with a small, fixed membership -- i.e. 3 to 7 servers. Everybody else is a client. In contrast, the blockchain is for a huge, frequently changing membership.
- Paxos is expensive and is used within a single data center with LAN latency. The blockchain is used in the exact opposite situation: on the Internet with large latencies and large variance in latency.