I am right handed and set my hi-hats on the left side and my ride cymbal on the right side, but I play both cross-hand and open hand on the hi-hat cymbals. For me it just depends on what the tune being played requires my right hand to be doing (i.e. a repeating pattern on snare and toms with my right hand).

HOWEVER, I only use one set of hi-hats so I've just developed the ability to switch to open-handed (when needed) over many years of playing. the open-handed style is not my "usual way" of playing....just when needed.

I also mount my cowbell on the hi-hat stand (on my left side) because it gives me the option of playing it with either hand (again, according to the requires of the tune).

AS far as recommendations about playing opened-handed as opposed to cross-handed......everyone has to play in a manner that is best for them. One or the other?.....both?. I say do your own thing your own way.
