X and Y are better options for jumping because they offer better control of the jump, both in terms of momentum and height. Personally, even if you're already used to using "Tap Jump" (control stick), I would advise swapping to using X/Y. I used tap jump for 10 straight years, but for the reasons below, I endured the struggle of breaking the bad habit over 3-4 weeks of daily practice. It's your choice at the end of the day, but I can honestly say from my experience that it's really helpful to make the swap.
When jumping you can determine how far you wish to move horizontally by holding left/right on the control stick at the same time you jump. With the control stick, I believe maximum horizontal momentum isn't possible, since you have to hold it slightly upwards to have the controller register the jump as well...but even if it is, you could imagine the harder difficulty. Alternatively, you can just hold it all the way and then press X/Y. This is easiest to test out with Captain Falcon, if you want to see for yourself.
Concerning height, Short Hops are much easier to input using X/Y. SHs are essential for SHFFLs, a basic tech that's necessary to just about any character to some degree in competitive play, or even better casual play. They are inputted by pressing a jump button to initiate the jump-squat animation (easiest to see when using Bowser), and then releasing the jump button before they leave the ground. If done correctly, the character will jump a shorter distance than usual. This is easy for X/Y button users because you simply have to tap the button. For control stick users, you have to move it upwards (supposedly considering the direction as well), and then move your finger off of it quick enough for the control stick to return to it's neutral position itself; an action that may be affected by how worn down and used the control stick is.
Z is often the button of choice for grabs, since it enables the use of Jump-Cancelled Grabs (Jump > Z to cancel the jump-squat animation) and Dash-Cancelled Grabs (Dash Attack > Z to cancel the DA animation). R/L+A is commonly only used to Shield-Grab; a common tactic is to shield an attack with R/L, and then pressing A to initiate the grab once the opponent's attack hits the shield and is within grab range.
