Both of these serve as a mechanism to notify once the user enters/exits a given point of interest. What are the pros and cons of each ?
Coming from someone who switched over to Google Play Services a while ago, i can give you some experiences:
I have an app, about 2,5 years old, that uses location services extensively. From the outset, of course, we used the LocationManager since that's what was available on the Android platform.
We had a pretty bad experience with Location Services on Android compared to IOS. It was buggy, unreliable, and gave less precise locations than than our IOS app, plus that it drained more battery. It was a drag.
Therefor, when Google unveiled the new API in june this summer, we jumped at it. It is way better. A couple of things:
So, when it comes to the location output and work, everything is better. But there are some downsides:
You have to have Google Play Services installed, meaning it wont work on any "non-google-approved" phone models, and in some instances you'll have to tell users they need to install it.
The API itself is more complex IMO, in part due to point 1. In addition to the "regular" callbacks i.e. waiting for location fixes etc. You now have a process that takes part before you can get started where you have to check that playservices is available, and "connect" the locationclient. This is extra code and a bit more complex to grasp. More faulty conditions to take into account in the code too (if you can be bothered...)
Google play services itself requires at least 2.2 so it won't work for older devices than that. We had to tell some clients they had to upgrade...
Hope this helps.