I wouldn't really consider SDL2 and SFML to be 'engines'. They are pretty thin layers to abstract away platform-specifics and give you access to basic 2D drawing capabilities. Anything beyond what is provided in the box, you'll have to roll yourself (which will almost certainly involve learning OpenGL).

Honestly, I'd recommend Unity. I appreciate it isn't C++, but the feature set is pretty hard to beat. Especially the click-once to deploy to android, iOS, etc.

You should have a look at cocos2d-x, I think it is quite nice: http://www.cocos2d-x.org/

It has a very easy to use API, very straight forward. It also has some editor, but I haven't really used that so can't tell how good or bad that is.

Well, though GameMaker isn't what you are looking for, I have to refute your mentality that it isn't "programming." In fact, the GML language is much more than a bit of drag&drop, and isn't something you should take so lightly before getting better informed.

Unity is also something to look at, though it also isn't C++. Also, it is somewhat like throwing a jackhammer at a small nail in that it does much more than a 2d game. That can be a good thing though, as it is a pretty good system to get into, and would allow you to move into 3d pretty easily, using the same skillset and programming language.

Hello,

As the title suggests I am looking for a suitable game engine. We are 3 programmers that have never made a game before but now want to create a complete game. The game will have: C++, 2D graphics, top down view, Real time action and a story component.
Sadly I failed to find a real engine which uses C++ and still allows modifying components to better fit into our game.
Thank you in advance for helping us.

Can you give a little more context of what you need?

I have been using orx (http://orx-project.org/) for 3 years, it is written on C, but has a C++ shell as well (called Scroll) and brings a lot to the table such as support for animations, sound, particle effects, FX* and time tracks**.

It is core idea is to have objects described on ini files and create/control them via source.

It has a small, but very active community (which now I am a part of) and questions on the forum/gitter are answered pretty fast.

* Basically it changes an attribute of an object for a given period of time, very useful for small effects. For instance, you can use it to change an object alpha, which causes a blinking effect, that serves as an enemy death effect.

** A scripted series of time based events.