Yes, of course can bigger textures give better quality. (?)
Even if you are using mipmapping do you probably get better results if you also are applying a detail texture.
Mip mapping won’t give you better detail when closer, it will reduce crawling when you’re far away. And if you use bigger tiles, you can have fewer tiles, which means that you’ll have less variation so it might look a bit more repetetive. 16 pixels is probably on the small side though, that’s what I used when I used to do stuff on my amiga in 340x256 resoloution.
I thought you were talking about 2d tiles, not the size of textures. You can safely use 256x256 textures on just about all hardware, and if you’ve got a newer card you can go much higher. Unreal uses detail mapping, i.e. it modulates the texture by a second detail texture when you’re close to add high frequency detail.