Anesthetic. It is all very relative to what the procedure is you are having done. Most of the anesthetics used the strength is not the issue, but rather the duration. There are anesthetics with Epinephrine in it which is a good vasoconstrictor and holds the anesthetic in that area for a longer period of time. There are also anesthetics with no vasoconstrictor if you don't need to be numb very long.
Local anesthetics. Most dentists only supply themselves with a few types of local anesthetics as the "strength" ; duration are pretty similar. There are ultra-long lasting local anesthetics but generally only used for difficult surgical procedures. The difference is mostly whether or not it has Epinephrine in it which decreases bleeding ; extends the time of anesthesia. All should work equally well for procedure.