I tend to prefer bags with a zipper closure. If it's an open top bag, a magnetic snap does help a great deal, IMHO, at least as far as restricting access for possible pickpockets. Having things roll out is a whole other ballgame, but I'm usually conscious enough of how bags sit that it's not a major issue for me for my day-to-day use. If I'm travelling, I'd definitely choose a bag with a more secure closure, though, e.g. zipper or a large flap. For open top bags without magnetic snaps, I'd also usually at least try to make sure it's deep enough that pickpockets can't reach in too easily to snatch my wallet, phone, etc.
Specifically WRT the RM Nikki, though, it seems like it should still be fairly secure since the top is meant to fold down in order for you to wear it properly. I just probably wouldn't use it when travelling, since laying it flat when you're going through security or when you're on the plane definitely increases the likelihood that something could fall out.