For a cut-the-rope style game, GameMaker is probably the best style of game engine.

For a side scroller type game, Unity's 2D shows a lot of promise. You may or may not choose it after looking closely, but that is up to you.

They are right that the engine is still fundamentally 3D. The 2D is just a view along the Z axis, plus tools for sprites, sprite sheets, and sprite-based animations. The interesting thing about it is that the 2D and 3D components can live together. So if you want to throw a 3D thing into a sprite-based world you can do that.

Another engine you might like to try out is Stencyl. Created for flash games, but has broadened it's scope now that flash is losing most of it's market support.

I haven't used Game Maker - but Unity and Stencyl are my top 2 of those that I have used.

If you're in doubt about a solution (in this case, Unity), don't rush and try to make your dream project with it.

Make a smaller, easier project (like a clone of some classic game) for you to learn about the engine and see if it meets your needs.

I've used Unity for a couple projects. The pro's to Unity are pretty obvious and have been listed en masse by the above people. Here are the cons, as I've seen them.

--NavMesh's and NavAgents are unavailable in the free edition. This means it's up to you to code your own pathfinding in a 3D environment.

--Point lights are a bit awkward. If I put a point light up in a building, I can see it illuminate the ground outside the building for some reason.

--Dynamic shadows only available via one directional light in the free version.

--MecAnim system is a little touchy, in my limited experiences with it. Your 3d models and armatures have to be correctly positioned for it to recognize them when importing.

Now... ask yourself, how many of these cons even apply to the game project you're about to do?