Nice question ...usually plants are treated with nitrate or ammonium , both a sprefered surce of nitrogen , however amino acid is another potetn source of nitrogen supply.The uptake of amino acids by plants is more advantageous energetically, when compared to the absorption of nitrates or ammonium, because the plant does not need energy to assimilate the absorbed nitrogen and later incorporate it into amino acids . However, the capacity of the amino acids to be absorbed by the roots is closely linked to their availability in the rhizosphere and to the activity of amino acid transporters in cell membranes in contact with the soil solution .

The better root growth favored by the addition of amino acids can enhance the biologic nitrogen fixation, which leads to a greater production of ureides. Furthermore, with the larger root surface the nutrient uptake can also be increased, as for example, the nitrate. The nitrogen metabolism can also be altered due to the signaling role promoted by the amino acids. ( relevant PDF enclosed for furtehr reading )

It is suggested that viable roots use free amino acids from the soil and that the main flux of carbon to the rhizosphere might be in the form of organic acids.(Plant and Soil volume 109, pages181–188 (1988))

What do you mean by "preferred"?

As we can't ask the plant directly, we can run experiments to measure uptake rates across membranes or surfaces etc. and while I'm sure there are results claiming leaves have higher rates than roots and vice versa, the likelihood of there ever being enough amino acids in the aerial environment to support a measurable amount of growth increase is pretty small, even accounting for dead insects, sap and animal wastes. Consider how much biological material (including amino acids) is turned over in a functioning soil ecosystem: most probably orders of magnitude greater than the leaves would ever experience. Reabsorption from senescent leaves might be the only comparable measurement.

Which is a long-winded way of saying, even if leaves did absorb amino acids faster than root, there is a much greater supply for the roots present in the soil. Slow and steady vs short and fast.

NB no data or references to support this, I am prepared to have this idea disproved.

While comparing all three form of N-supply to plants viz., nitrates , ammonium and amino acids , nitrates are usally the preferred form of N ( we debated at length long back , we can refer that great discussion on RG ) by plant roots ( since it is less energy consuming process) , with an exception of crops like rice ( ammonium as prefered nitrogen form , upland or submered paddy ) . Despite the amino acids tranporters identified within the roots , i feel , regardless of absorption sites ( roots or leaves) , amino acids would be a a harder choice for plant roots or foliage over nitrates or ammonium , for the simple reasons , amino acids molecular/ionic size would be much bigger . However , there are number of evidences about direct uptake of organic ions by plant roots , especially amino acids. When it comes to concentration of amino acids in soil solution , in case , amino acids concentration overtakes the concentration of ammonium and nitrates , could be a specific soil olution ionic equilibrium condition where amino acids find a preferrred choice by plant roots . may be passively absorbed...

Roots!