Riding the bike, the only thing you would potentially notice is if there's any difference between the rate of engagement of the two ratcheting mechanisms being compared, i.e. that specific freehub versus specific freewheel, and also any differences in how noisy they are. Examples exist of each that are more or less noisy or quick-engaging, so there is no universal answer.
Cassette hubs made for derailer use and converted to singlespeed via spacer kits have the disadvantage of being weaker and less laterally stiff than dedicated singlespeed hubs, because the drive side bracing angle is steeper and there's less total spoke tension. That could be noticeable depending on the rider and circumstances, especially if you're pushing what your chosen rim can handle strength and stiffness wise.