For single adjustment probes, it doesn't matter which end [ although in theory, the BNC end gets less banged about, if you treat your probes roughly]. However, if you have adjustments on both ends: BNC
and probe handle, chances are it has both high and low frequency compensation. The 2-end adjustment probes are often more costly, and typically have higher frequency response than single adjusts. The high-end compensation is rarely adjusted compared to the low end. Some probes has both adjustments on the BNC end, and can have 2 - 3 adjust screws.
Its good practice to check compensation before each daily use or if you are skeptical of any result; since its basically an adjustable cap changes in ambient temperature can make it drift about. Most of the time you'll just check the compensation, and not need to adjust it.
Hi I am looking at oscilloscope probes and some of them have the trim adjustment in the probes and others at the BNC. end and some I have seen even have them at both ends. What I have no idea of is which layout is best and why. Do I go for the ones with the trims in the probe or the BNC. Or are the one with adjustment both ends better and are those harder to adjust. Which is most likely to get out of adjustment sooner etc. All thought on this are most useful.