Edmonds-Karp is not the fastest. Dinic's algorithm runs in time. Push-relabel algorithms can achieve or better. For competitive programming, Edmonds-Karp is usually fast enough unless and are huge (over ,).
Dinic's is faster but more complex to code. If time limits are tight, consider Dinic's. Otherwise, stick with Edmonds-Karp. It is simpler and less bug-prone. Know when the extra complexity is worth it.
Space complexity is for the data structures used.