I was taking a snap on a sunny day, and the subject was in front of light source and subject was shadowed out(or blackened) In this case is it better to use partial/spot metering mode (zoom in to face lock exposure zoom out, reframe, click) or increase exposure compensation. Or are both the same ? If not what's the difference between these two approaches?
Short answer: what you want to do is to switch to spot metering mode, place the face of your subject in the exact center of the frame (no need to zoom in unless the subject's face is really small in the picture), press exposure lock, reframe and take the shot - now the subject will be properly expose and the background will be over-exposed.
In the "smart" metering mode (Canon calls it evaluative, Nikon calls it matrix) the camera looks at the entire image, apply some magic formula and decides on a setting that work for the entire frame, this is great but if there's something very bright or very dark in the picture it can throw the exposure off since the camera doesn't really know what the impotent area is and what kind of picture you want to take.
In spot metering mode the camera only looks at a tiny area in the center of the frame and decides exposure based on that, this let you decide what is properly exposed (and let the rest of the picture's exposure falls where it is relative to the area you meter on).
The other metering modes are not nearly as useful as those two and I suggest not to use them unless you have a specific need.
Exposure compensation is a different but somewhat related concept, after the camera decides what the "right" exposure is based on the metering mode you can override it and tell it the picture should be brighter or darker - this is useful if whatever you are spot metering on is not medium brightness or if you just want to make the picture brighter or darker (just because you think it makes it look better).
And finally, there's manual mode, in manual mode you set the exposure in absolute terms and not relative to the camera's decision - it sounds a little scary at first but usually in difficult lighting it's just simpler to switch to manual mode and set everything yourself (you can usually see the camera's metering when in manual mode - so you can set your initial values based on the camera's meter and then you don't care if something bright or dark suddenly crosses your frame or if your subject is really in the spot metering area or not and if your exposure lock is on or off)
Either of these approaches will work fine. You should use whichever works more naturally for you.
With the spot metering approach, what you're doing is looking for something which has the tone which you would like to make the middle/neutral key for the image. That's what the metering system does. If you want the object you meter from to be brighter or darker than middle-gray, you would combine this with positive or negative exposure compensation.
Your workflow when using exposure compensation in other metering modes will depend slightly on the mode used and your knowledge of it. With center-weighted or full frame average metering, you can fairly easily judge if the scene as a whole is brighter or darker than average, and particularly whether your key subject is brighter or darker than that average. Then, you use exposure compensation to tell the camera what you want.
With matrix metering (also called "evaluative" or "zone" metering), the camera tries to be smart. It will recognize patterns in the scene and automatically decide if a higher or lower exposure is appropriate. A very common one is recognizing a bright strip across the top of the frame as the sky, and effectively ignoring it while exposing for the rest of the frame. Until you become very familiar with what your make and model of camera will do in a particular situation, it's hard to know when compensation will be wanted. Here, you can take test shots and watch the image histogram, eventually learning to "feel" what the camera will do. Usually, one learns to either a) trust one's camera's matrix metering and only apply EV compensation in particular, known circumstances where it gets it wrong (for example, a snowy landscape), or b) not trust it at all, and use center-weighted instead.