I cannot speak for everyone, but I think my beard made me more approachable. When I would have a stubble most women usually assumed I was a typical %+$!*@+%#, no idea why though. I would hit it off with some girls but that took a lot of effort from my side convincing them I am not a typical douche.  


Last time time I grew my beard was a year ago and it wasn't as big as it is now, but girls would usually step up to me even though I thought it made me look more aggressive. I don't go out a lot these days, but I went out last Thursday and some girl who was with some beardless guy approached me and opened with: I really cannot withstand a man with a beard.  Needless to say though I didn't pursue her, but 30 minutes later some other girl just grabbed my hand and started dancing with me and then some. Really, this almost never happens when I have a "Douchy" stubble. 

One thing I always keep in check though is grooming the beard, and oiling it for softness. Make sure the beard style you choose compliments your facial form and features. I'm in my mid twenties though, not sure if it matters a lot