Over here on the west side of the cap desert willows wait several days longer than mesquites to put on leaves. We had a big desert willow that I climbed around in as kid growing up on the east side of the cap but I can't remember if it leafed out a little later than the mesquites or not. I'm a thousand feet higher in elevation here and that may have something to do with it.
I had been getting one and two year old mesquites with weed-be-gone until this year and it no longer worked. The reason is they cut the percentage of 2-4-D way down in the new stuff and also raised the price. Crossbow contains almost four times as much 2-4-D as weed-be-gone now and one other chemical is different and it costs a little less. I applied it to the larger bush just as the instructions said, spray the trunk 18 to 24 inches above the ground and around the base.
After I left home my dad killed a large number of much larger mesquites than grow here with a hatchet and kerosene. He chopped thru the bark around the tree and soaked the cut with kerosene. Of course mesquites, being a very invasive species, have returned in the 50 years or so since he did it.