Ammonium Nitrate is Ammonium Nitrate. And
Urea is Urea. So as long as the NPK is the
same and these chemicals aren't bundled with
some other chemical herbicide then store
brands are essentially the same as name
brands.

jos14h, the whole issue centers around Nitrogen. There are a very few synthetic sources of Nitrogen and all of them are very soluble. They do not last long in the ground. The formulators treat urea (42%N and very soluble) to make it slowly available. This is blended with with something like untreated urea or ammonium sulfate and sold to you and me. This information is on the label. The encapsulation or sulfur coating or whatever process is used adds to the price of the fertilizer. Soluble fertilizers like "Miracle-Gro" and the like are totally soluble and that is why we have to apply them so frequently. The commercial guys go for the highest N content (say 38-15-15) and the highest proportion of this to be slowly available. (say 50%). They will pay a high price for it but one application may last as much as 8 weeks. In the above formulation there is 38lb. of nitrogen in a 100 lb. bag. At 1 lb. N per 1000sq.ft. it will cover 38000sq.ft. 19 lb of nitrogen will be immediately available and your lawn will green up starting tomorrow for the next month or so. All the soluble stuff will be gone but by then the slow release will start to break down (temp., uv waves, water) and make more N available. I do not know that this answers your questions. I do not know that there is a cut and dried answer but I did enjoy the challenge to my memory.
OK, I did have to look up one or two things.

I am not a Scott's fan for two reasons.
Price & a complete lack of formulations.

But to answer your question neither is better, they are equal except in price assuming the NPK ratio is the same.

My biggest gripe is the lack of custom formulations and one missing ingredient phosphorus. ScottÂs formulates their product for Midwestern soils where the product is made and the soil is naturally rich in Phosphorous. Plus if you want a slow release urea type, there is no choice in what percentage of slow release to fast release nitrogen. You have to take what they give you at a premium price.

For example a professional supplier like LESCO has any NPK ratio you would ever think of, and in any ratio of slow to fast release nitrogen. Plus if you want some weed-n-feed product, Lesco has just about any type you want blended in, not just Pendimethalin(what Scott calls Halts).