Yes, there's a point where one becomes 'better' than the other, but for rotating mechanical objects (such as a fan) time period measurement is generally far preferable - pulse counting is far too slow!.
For example, if you want 1Hz resolution then it takes 1 second per reading, or for 0.1Hz resolution it takes 10 seconds per reading. Using time period measurement only takes the time of a single pulse, no matter what the resolution.
For an example, if a device is rotating at 6000 rpm, then pulse counting per second will be 1% accurate, if the same device rotates at 600 rpm, the accuracy drops to only 10%.
If you check the (VERY old) MicroChip frequency counter application, it auto-switches between the two, using the best whatever the incoming frequency.