FusedLocationProvider uses a mix of hardware to determine location based on the context of the request, meaning it's optimized transparently to you. It will also cache captured locations between applications to avoid unnecessary work to determine location info. So if a user has a variety of location-aware apps, they potentially avoid taxing the device (and waiting) for a location capture as one may have already been cached.
While the ol' LocationManager will suffice in small, one-off situations, you should definitely consider the newer alternative as the benefits may be great, and the work to implement, easy.
You may as well use it as Google Play Services is regularly updated across devices, and continuously includes improvements to location-based features (and more).
A link to an explanation of the FusedLocationProvider at launch: https://www.youtube.com/watch?v=Bte_GHuxUGc
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