But here is how I see it on my high pH heavy clay soil raising perennial hay crops.

any major preference between NH₃, urea, or liquid? I've always used NH₃.

Other than price, no. not if applied according to the rules of nitrogen fertilizers.

Personally I prefere injecting anhydrous into my grass hay meadows. If and when I need to use liquid or dry I will surface band the product.

Other than costing less per pound of N, NH3 being another cation will tie up in our clay soil and become a slow release fertilizer. Any N not used this season will become part of our residual nitrogen bank and be even more slowly available to my grass hay crop.

Liquid has roughly half it's N in nitrate form. This needs to be used soon, which effects the timing of the application.

I also use liquid phosphate at the same time we inject the AA into the sod.

I suspect your soil, climate & management is different, so what I do may not apply.

I am hoping for some one to respond so I could learn how they do things.