I used to play 2D games when I was a kid, because most of the games were 2D that time. I saw the 3D boom, how it become popular and how people even thought 2D games were dead.
Speaking of aristic approach, 3D with 'photorealistic textures' are still far from perfection, but there're some games made with stylish cartoonish look, and they are visually appealing even when they get technically old. Compare, say, Unreal Tournament 3 and Borderlands series - both games use the same engine (UT3), but UT3 now look a bit dated, while Borderlands remains stylish and sweet.
On technical side, modern 2D games made in HD can look very artistic and beautiful, so they don't have to have big pixels everywhere. This somehow blurs the visual difference between 2D and 3D, and the 3rd dimension becomes more a design element, than the 'must have feature'. Look at many fighting games, which use 3D models while being actually 2D gameplay-wise.
When I desided to finally try game making myself, I gave it some thoughts about 3D/2D and engine. To me, the most important thing was the ability to create game graphics myself in reasonable time, and, another important thing, the game shall run on every platform, be it a laptop, or tablet, or even phone. So, the answer was 2D HTML5 game.