I do not want to write the engine myself. I would gladly use an engine that already exists. With that in mind, would 3D still be more difficult to program than 2D?
Good to read that you are making a game and not an engine. There is a significant difference between writing a 3D engine and a 2D engine, but assuming you have a good engine, the only major differences become the art and spatial manipulation.
Note that it is not easy to build a game. Even simple hobby games can require hundreds of hours of work, and polished hobby games frequently require several thousand hours of work from an experienced developer.
Difficulty must be measured on that scale. If you are already investing one or more years into making a game, how much more difficult is 2D than 3D?
Assuming you have an existing and solid engine in place already, both 2D and 3D engines will basically have functions to play animations, functions to move things around, functions to add and remove objects from the world, and to otherwise handle game management tasks. In that regard there is very little difference between the two.
Again assuming an solid engine, some of the math is a little bit more complex. You need to have a reasonable understanding of linear algebra if you are going to manipulate things in 3D space, you only need geometry to move things in 2D space. There is some difference, but it isn't much of a difference when you consider the scale of a game. The extent of the difference is mostly a matter of your game design and how far your design deviates from the engine's functionality.
The art is the biggest difference. Creating tens of thousands of sprites is tedious and labor intensive, and is not inexpensive if you choose to contract it out. Creating models and textures and animations in 3D is somewhat less labor intensive, less expensive, and usually much faster.
Finally, as was touched on by a few posts, you need to consider the nature of the game. A game like Braid was a game designed around replaying the level backward and forward over time; doing this in 2D means recording and replaying much less data then a 3D world. Physics-driven games typically require dynamic motion and animation, such a thing is better suited for a 3D game since it is unlikely your 2D pixel artists can reasonably draw all such combinations.
Any path you follow will have difficulties. 2D or 3D is just one implementation detail among thousands. It is more about choosing a set of difficulties that gives you the best chance to complete your project.
