Do you mean that in casual speech “mnoho” is generally used more rarely comparing to “veľa”, or is it just as regards ľudí/people?
I meant generally.
As usual, you made me think about it more and I think the situation is really so clear-cut only in the nominative and accusative.
"Veľa" is normal, "mnoho" sounds a bit formal or old-fashioned.
Videl som veľa zaujímavých miest. (normal)
Videl som mnoho zaujímavých miest. (a bit bookish)
Videl som mnohé zaujímavé miesta. (still bookish, and I agree with
@francisgranada that there is a slight difference in meaning - perhaps you are going to talk about some of the interesting places individually, perhaps you are going to make a contrast with other interesting places that you haven't seen...)
But perhaps because the indeclinability of "veľa", the declined forms of "mnoho" sound much more OK in casual speech in other grammatical cases than in nominative and accusative. Also "mnohí" means "mnohí ľudia", which allows you to save a word:
Veľa ľuďom to neprekáža. = Mnohým ľuďom to neprekáža. = Mnohým to neprekáža.
Here I still feel a slight increase in formality from left to right but not much.