I've seen two drills - one 600W the other 700W. Both 0-3000 rpm. But for 600W some guy said it can't make it with concrete, while for 700W reviews say that it does it. Both are hammer drills. I'm not mentioning models as the site isn't about product recommendation and anyway I want to learn how to choose them.
More important than the power rating is the type of hammer drill. This is a very useful link which explains the full difference between a 'Hammer Drill' and a 'Rotary Hammer'.
The former achieves the hammer action by spinning a bumpy disk against the end of the driveshaft of the chuck, which makes is vibrate a bit. These are OK for soft brick, but not much else. If you hit a piece of flint in some concrete, it will just stop, or cause the drill to wander into a softer area.
If you're going to be drilling concrete, you'd be much better off with the latter type. This uses a piston which hammers directly onto the rear of the drill bit, which slides in the chuck (this is also commonly referred to as 'SDS', for the type of chuck).
When comparing this type of drill you will usually find that, as well as power rating, they have the impact energy in kJ (kiloJoules) quoted. Obviously bigger is better. Most can also have the chuck locked so that it can also be used for chiselling, tile removing etc.
IMO - if you are going to be drilling concrete, you would be well advised to pick an SDS drill. You won't regret it.
P.S. As noted in the comments: Both are routinely described as "Hammer Drills". The distinguishing feature of the better type is the SDS chuck.
The only way I would go by sorting this out nowadays if I was new to this sort of stuff, is reading reviews.
With my experience I have owned a number of hammer drills which should go through concrete but didn't. I find that these types of tools are investments and quality is key.
To try to answer in my non technical fashion, more wattage, more power to transfer rotational force into impact force. If the impact isn't strong enough, the drill will not go through the toughest concrete, as I have experienced.