Since power yoga includes many postures which involves lifting self body weight. For example 5th step of Surya Namskar makes one bearing whole body weight on arms,shoulder and feet fingers. There are many such Asans like Kandrasan, sarvangasana, halasana, naukasana etc. Each of these Asans have postures which centers body weight on a particular body part. So are these as effective as lifting weights in gym because here one is lifting own body weight for several stretched period of times in one session of an hour? Will they improve muscle mass thus Resting Metabolic Rate (RMR) ?
No, power yoga does not offer the same benefits as weight training. I'm not saying one is better than the other, but one thing that is not satisfied by power yoga, is progressive overload by increasing resistance.
In weight training, this is one of the two primary markers of progress, alongside increasing repetitions.
But again, I'm not saying one is better than the other. Power yoga is far better when it comes to developing flexibility, for example.
All in all, which one you choose should be decided by what goals you wish you achieve. And if in doubt, do both!
Depends what you mean by effective. You asked at the end about improving your RMR via increased muscle mass. In terms of this, it doesn't even come close to strength/weight training. Alec mentioned a very key aspect for this, but it's even more fundamental than that.
You break down most of your muscle fibres during the eccentric part of an exercise (the lowering part of the bench press or the dumbbell curl for example). The eccentric part of an exercise compared to the concentric (lifting) and isometric(static) is MUCH more effective and efficient for muscle building purposes. Note that I'm not saying you CAN'T build muscle with isometrics and concentrics, it's just way harder. And since power yoga is mostly isometrics, it can't be considered equivalent to weight training, at least for muscle building purposes for higher RMR.
There are actually a lot more factors than this, for example, hypertrophy has been shown to be caused by tension, time under tension, progressive overload, and metabolic stress. All of these are more efficiently worked on via weights. Moreover, weight training promotes the release of certain anabolic hormones such as hgh, testosterone, improves insulin sensitivity (insulin is very important for building muscle), as well as protein synthesis.
This is only in terms of building muscle. In that regard, they can't be compared. But like Alec said for flexibility and basic strength, you can certainly get away with it.