Breville has gotten much better than they were just 4-5 years ago, but are still more of an appliance than purely coffee driven if that makes sense. They do offer innovative features, have improved the temperature stability in their lineup, include many extras often overlooked by most manufacturers, etc., but their main issues are longevity and parts availability for those that like to repair things themselves.
The Gaggia Classic is a good solid/capable machine that will last a long time and simply work the way it was intended.
Regardless of what you buy do you have a capable grinder and intend to use fresh coffee as both things are necessary to obtain good results consistently?!?