I've heard/read many times that shortest path problem is P, but longest path problem is NP-hard. But I have a problem with this: we say longest path problem is NP-hard because of graphs with positive cycles. But if you think about graphs with one or more negative cycles, we don't have any polynomial time algorithm for the shortest simple path either. In fact, once can be reduced to another.
To summarize, we can find a shortest/longest simple path only if there are no negative/positive cycles. Also we can detect negative/positive cycles with Bellman-Ford in both cases. So under identical criteria, both problems should be considered NP-hard.