Answering the question directly:
Generally speaking effective weight training increases your metabolic rate and yoga will decrease it.
Yoga is primarily an aerobic activity and can be strenuous or easy, and it can be for short or long intervals. Weight training can target multiple large muscles several times a week, or it can be a hodge-podge of random exercises in a gym (which is unfortunately very common).
A large advantage in weight training (resistance training) is that your basal metabolic rate will increase, you can read up on it in this 1998 study.
In summary, the findings of this study show that 10 wk of concurrent
resistance and endurance training have beneficial effects on energy
expenditure and weight loss.
Interestingly enough, and this has been found in two different peer-reviewed studies (2006 and 2008), yoga decreases metabolic rate.
The BMR of the yoga practitioners was significantly lower than that of
the non-yoga group, and was lower by about 13 % when adjusted for body
weight (P < 0.001). This difference persisted when the groups were
stratified by gender; however, the difference in BMR adjusted for body
weight was greater in women than men (about 8 and 18% respectively).
This doesn't mean that weight training will make you ripped and yoga will make you fat.
Yoga is a terrific activity, and additional research will probably show reduced appetite and other factors that come into play from yoga (although I'm being entirely speculative).
More than demonizing yoga, these studies to me show the effectiveness in strength training. By increasing the amount of calories that your body needs to just "keep the lights on", and shifting your diet towards protein and fat and away from carbohydrates, you will be on a great path towards reducing total body fat.
Spot reduction (removing fat from some particular area of your body) is a myth.
For flat/4-pack/6-pack/toned abs you need low body fat, and secondarily well developed ab muscles. Put your primary focus on reducing body fat, and as the evidence shows strength training is a great way to get there.