Single texture: Less quality, more intricate UV mapping but smaller filesize and better file management.
Multiple textures: Higher quality, simpler UVs but larger (total) filesize and worse file management.
Rule of thumb for single texture files is to let important areas take precedence over less important areas to maximize texture space efficiency. Like say the bottom of the feet gets less texture space than the top since the former is less likely to be seen and if it is it's usually short and takes up a small area of the screen.
For multiple textures, items requiring less texture space can be fitted into a single texture while the more important ones gets their own texture files. Just be aware of the filesizes.
For instance, a box with six sides can be textured in three standard ways. Firstly, you can layer the UVs of each side on top of each other. That way, each side gets a high resolution texture at the cost of uniqueness. Secondly, you can layer the six sides side by side. That way, each side can be unique but the side will have a smaller resolution. Thirdly and more next-gen, is to do the previous one but bump up the resolution of the texture file to get high resolution texture of the sides of the box at the cost of filesize. A fourth, more unorthodox way in this case, would be to give each side their own texture with multiple files. It will have roughly the same total filesize as the next-gen method but it will require a bit more work moving those files.