Most of the time, when guys are doing barbell training they are also doing a few body weight exercises at the same time. Mostly chinups/pullups and dips.
I'd say do both.
In my personal, old lady opinion, body weight stuff didn't get me very far. I still am not very good at any of it. But the barbells work for me. I've gotten 3 unsolicited comments about my physique in the last week. It has taken about 6 months. I suspect that my recent improvements are due to adding olympic lifting and subtracting wine and chocolate.
Female, 5'3", 49, Starting weight: 163lbs. Current weight: 135 (more or less).
Starting squat: 45lbs. Current squat: 180 x 2. Current Deadlift: 230 x 2