JIm,
You've heard it both ways because it depends. There are far to many variables to, IMO, state catagorically that one is better than the other. For example, we often hear, and fairly accurately so, mostly in single pass welds, that slower travel speeds, by increasing heat input, enlarges grains, which is generally considered detrimental to impact results. However, slower travel speeds can also increase depth of recrystallization in multipass welds thereby improving impact results. Slower travel speeds can vary the oxide relationship in fluxed process weld deposits and thereby improve impact results as well.
The general industry practice utilizing heat input formulas and maximums is a sledge hammer. There is no replacing actually running tests and getting results, which is why we are still required to actually run tests and get results.