Should I use PendingIntent.getService() or getBroadcast with AlarmManager?

One uses PendingIntent.getBroadcast() to call a broadcast receiver when the alarm goes off and inside that receiver the service to do the real work is started.

it has one more step in starting service than

Another approach is to use PendingIntent.getService() and call the service directly when that alarm goes off.

then you should use the second approach as it is reducing your one step in execution..

Reading your edit I presume you found out yourself: If you want to make sure that your service is started when using AlarmManager, you better take the detour of first sending to a receiver and acquiring a wake lock there. Otherwise it is possible that the phone will sleep before the requested service is launched. That's what the javadoc of AlarmManager says and I also read it in post by Google engineer.

So now for your edit: When to acquire the lock? The whole point of using the receiver is to acquire the lock within the onReceive() method of the receiver, because Android will not fall asleep during the execution of this method.

For an example see this question.