The reason you see two different causes above (essentially friction and adjustment) is that the fix depends on where you are experiencing the delay. If the delay happens when you are shifting to higher gears (smaller cogs) then the problem is friction, because on those shifts it it the derailleur spring pulling the cable that is completing the shift. If it happens when shifting to higher gears (larger cogs) then it is an adjustment issue. Adjustment cannot make the shift in both directions slow, and only very high friction could cause a slow shift in both directions. If you are somehow experiencing delay in both directions then either you have both of the above problems or something is seriously wrong with your shift lever.