Holding over or under and using a reticle to shoot with, rather than dialing elevation requires many things. Most importantly among them is proper scope mounting. If you have the smallest amount of cant in your scope, it won't work. Then you have to know exactly where the marks on your reticle intersect the bullet's line of flight. Whether you dial, or use the reticle, you have to know the elevation.
I find that for many applications, using the reticle is faster. BUT I still have to refer to the chart to see which mark in the reticle to put where. It only eliminates dialing, but it substitutes counting down to the proper hash mark for dialing. If there is alot of counting going on to find the right elevation hash mark, there isn't a significant speed advantage because of the time spent making sure you are on hash mark #7 rather than 5. Finding the center of the reticle is VERY fast...
Here is sort of how I do it using the Leupold Mk4 TMR reticle. There are hash marks at each mil, and half mil.
for example, if:
crosshair =100
bar 1 =186 half
BAR 2 =253 FULL MIL
bar 3 =362 half
BAR 4 =438 FULL MIL
bar 5 =497 half
BAR 6 =547 FULL MIL
with targets at the following distances, the hold is:
100 crosshair
200 bar 1 a bit hi
315 bar 2 at the bottom
378 bar 3 on the top
424 bar 4 half way to bottom of target
487 bar 5 just below center
500 bar 5 just above center
535 bar 6 just below center
I use the exbal program, and it has many of the most common reticles, and the program interfaces with other data I input to give me the impact points for various reticles. But like I said above, some times dialing is faster than searching your reticle for the precise hash mark to use.