Why the question?

The one in the coldest environment?
but seriously, I believe the distilled would freeze more quickly (or at least have the potential too) as tap water is more likely to contain contaminants that would increase the specific heat of the liquid. But, in general, I believe the difference in freezing would be minimal.

They must both start at the same average temperature.

The one that has the least dissolved gasses, ie., the distilled water will freeze first.

The water that isn`t moving will freeze first :) I doubt you would see much if any difference between tap and distilled otherwise.

Wouldn't moving water dissipate the heat from the inside of the volume more quickly, thus causing it to freeze more quickly?

Although the question posed "witch freezes first, tap water or distilled water" is somewhat interesting. It's hardly hydroponics related, that's why I originally asked "why the question" just in case they had a real reason for asking the question. But realistically there are many variables to consider. But assuming all the variables are exactly the same, I cant see there being much difference in the freezing times. Neither in the exact moment that they begin to freeze, or when they have become completely frozen.

The only thing that I can see making much difference is the salt content of the tap water, and that will vary from house to house, and city to city. So it's a variable that would need to be measured if someone were really wanting to do a real test. Another consideration is how precise you were wanting to get in the time of freezing. Down to the minute, second, thousandths of a seconds? Then you would need to deride just what you considered frozen, at the first signs of ice, all the way down to completely frozen in the center of the cube. If you decided that completely frozen was the standard you wanted to go with, that opens up a whole another discussion of just how to determine the exact moment when the center of an ice cube becomes frozen.

Remember all of that is not even taking into consideration all the variables like the freezer temperatures, how slow or fast the temperature drop is, volume of water to be frozen, type of containers the water is in in the first place (for instance metal will conduct heat faster than plastic) etc.. All in all, unless you wanted to get down to the exact second where there's a difference. Considering all the variables are exactly the same, the salt content would be the only thing I can see making enough of a difference to notice, and even that would need to be high to make much difference.

All else being equal, I would think that the one with the lowest Specific Gravity would freeze first, I would assume that to be the distilled water but I could be wrong. I have to agree that the difference in freezing time would be so minimal that it would be extremely difficult to measure.
But while we're on the subject of rhetorical theories, can anyone explain why ice gets colder when I add salt to it while making ice cream? I can't figure that one out for the life of me. Not a clue. I just can't comprehend it. Could it be an oxygen matrix?
Ken

I have not measured it, but don't believe it does get colder than the ices starting temp. Adding salt to the ice is about a chemical reaction and surface area, rather than changing the temp. This chemical reaction allows the ice be in a liquid state rather than a solid state while still remaining at the same temp (below freezing). And because it's in a liquid state, it will be in contact with the entire container, covering the entire surface area of it. Where a bunch of ice cubes wont be unless you froze them together. Ice cubes will have a lot of air pockets, air pockets insulate from the cold temp of the ice.

No air pockets, more surface area is at freezing temp at the same time, thus cooling the ice cream faster. Giving the illusion of being cooler. But it's just because it is still at freezing temperatures and in a liquid state. That is the same reason that mentioned salt content in the water of freezing ice. Not that it would be colder, but because saltwater will remain in a liquid state longer, thus taking longer, and/or needing to be colder before it becomes solid.

Test it, take two buckets, fill both of them with ice cubes. Take a pitcher of water and stick it in the freezer. Leave it there until it starts freezing on the edges. Then take it out and break up the ice that had formed. Basically making a large slushy of just water. Then pour it in one of the buckets, (no salt in anything), then stick one hand in one bucket and the other hand in the other bucket. Is there any doubt that the one with the water would feel colder faster? That's just because more of the surface area is being contacted. Ever drank a slurpee to fast and got brain freeze, same principal.

P.S. You can also make the same type of water slushy I mentioned earlier pour it in one glass. And take another glass (exactly the same) full of ice cubes. Then pour salt on the ice cubes until it gets good and slushy also. Then take two (exactly the same) thermometers, put them in both glasses at the same time. Then check them both at the same time (say about 5 min). I would be very surprised if the one with salt was any cooler. I would do it myself except I don't have two thermometers that are the same. If everything is not exactly the same (except the one variable), it would be hard to trust the results.

Another example,
I'm sure that everyone has herd of salting the roads to melt ice (black ice). They don't do it to make it colder, they do it for the chemical reaction that liquifies it, getting it off the road. Taking it from a solid state, to a liquid state.

Very good explanation indeed!
It seems I had misplaced the simple concept that cold is merely an absence of heat and not the other way around.
Its the cream that gets colder (closer to 32Deg.F) and not the ice/water surrounding it. The salt simply allows the ice to hold it's temperature in a liquid state thereby increasing contact area. I must have had brain freeze. I Probably would have figured it out had, I ever stuck a thermometer in it. Nothing voodoo about it!
Thanks,
Ken

It is clear from the multiple responses all explaining different different phenomena that the original question was asked without the proper information about the initial state of the water.

I still think the best response was homehydro's "Why the question?"

Actually, it was an invitation to idle chatter...... No science required.

Apparently, with 20-20 hign-site.
The original poster has not even felt the need to join in on there "idle chatter." So what's the point? To get other people to discuses there issues? The least they could have done is to join in on the conversation. Is that too much to ask? Apparently.