LAN Or MAN Which Is Faster?

It's subjective.

A LAN (Local Area Network) may appear faster to you because you're communicating with computers that are in the same office/building as you, very physically close, and the data won't have far to travel.

A MAN (Metropolitan Area Network) is a bunch of building-based LANs around a city, all connected together. The 'pipes' connecting the LANs together will be 'wider' (faster) but as the data will have farther to go, it may actually feel slower.

So - a MAN has faster pipes, but performance on a LAN may give you faster results.