Roots are my preference
Hi again.
Your question is a good one, and I will share what I have learned.
Nutrients enter plants in several ways. Foliar feedings are effective for certain plants and certain nutrients. Absorption thru some plants leaves (think thick cuticle, or hairy leaf) is very difficult, but of course, the foliar nutrients that are not absorbed drip off the leaf and land in the plants drip zone which is rich in nutrient seeking roots.
Soil applied nutrients have several issues. Some forms of nutrients must be metabolized by soil organisms to a form that the plant can absorb/use. Nutrient absorption is also a function of your soils texture (clay tends to "hold on" to nutrients more than sand, which allows them to pass thru relatively quickly), pH,and to some degree water and air in the soil. Additionally, some nutrients become "locked up" in the soil and unavailable to the plant. Iron is an example. Poorly absorbed at neutral to alkaline pH range, and tends to bind tightly to soil cations. Hence the chealated form, which basically keeps the iron from binding up in the soil and allows the plants to absorb it.
Foliar feeding avoids the soil binding and absorption problems. Most NON organic foliar fertilizer is readily absorbed without micro-orgainism intermediation. What is not absorbed falls on the drip line. Foliar feedings found a following when plants showed deficiency signs and a foliar application of that nutrient improved the plants stress. Iron, again, is an example. However, the effect is short lived and repeated applications must be made. Suggesting it is better if your plants have a deficiency, to correct the cause.
So, to answer your question, foliar is faster, soil is better long term, assuming you have healthy soil. Additionally, foliar feedings to excess may leave salt deposits on the leaves.
Hope that was enlightening, again not trying to preach
"The difference between good gardeners, and great gardeners is their soil." Unknown author, but my Mom preaches it.
Jeff