It could be ambient light blur if there's bright daylight coming through, but normal room lights won't have any effect.
It's more likely to be the flash duration, which is your effective shutter speed as you say, but TBH the t.5 figures that most manufacturers publish are frankly a lie - but they use them becuase they're an industry standard that makes them look better.
From my tests comparing flash durations to actual shutter speeds, as a very rough rule of thumb the visual effect in terms of 'action stopping potential' is somewhere around 2x the t.5 time, possibly up to 3x which is where the t.1 time usually sits.
More general rules of thumbs - effective flash durations will usually be shortest at full power with a studio head. But can vary, especially with battery packs, depending on how the capacitors are configured. Manufacturers' literature should be a decent guide on this.
For the shortest flash durations, hot-shoe guns are much better because of the way they clip the flash pulse at reduced output (good link posted above). Typically, you'll get a real 1/1500sec at half power and it gets shorter and shorter as output is reduced, down to 1/40,000sec in some cases.
One thing that generally distinguishes expensive studio heads from entry level kits is the shorter flash durations.
