On my knives that have both, I never use the thumbstuds for opening. And the one thing I really don't like about thumbstuds is that they sometimes get in the way when sharpening or stropping, colliding with the edge of the stone/strop. And the more poorly thought-out versions create other problems, like snagging on pockets and inadvertently opening in the pocket. A friend of mine is paraplegic, in a wheel chair. For a short while, he carried a thumb stud opener in his pants pocket. He promptly gave that up after the stud snagged the inside of his pocket and exposed the tip of the blade. He had no feeling in his legs, and didn't notice it until he saw the blood stain on his pants.
Given a choice, I'd be perfectly happy with the flipper alone. And, in the case of opening the knife a little more slowly or 'discreetly', this can be done one-handed with a well-thought-out, wide and fairly deep nail knick, without the studs hanging off the side of the blade.