Which type of rock is older and why?

Without looking at specific samples of rocks and comparing them, we can rely on a few general rules for dating rocks.
The Law of Superposition says rocks on the bottom of a sequence (a vertical cross-section of rock) will be the oldest, as new material usually accumulates on the top. There are definitely exceptions to this, such as plate tectonic activity that can go so far as to flip rock sequences completely upside-down, but this isn't very common and it's usually easy to recognize when it does happen.
Sometimes newer rock will protrude into older layers. Viewed from the side, this will appear like a spike or tube of rock that cuts through several layers, and those layers will be continuous on either side. If this is a volcanic layer, it's typically called a plutonic intrusion. In this case, the intrusion is younger than the layers it cuts through. 
In general, it's hard to say which rocks are older based on the type of rock themselves, but granites tend to be very old.
https://pubs.usgs.gov/gip/fossils/rocks-layers.html