I wonder how many cities your opponent would have by the time you met them.
On anything below Prince, they will usually have fewer than you so long as you actually try to expand in any way at all.
On Prince, they will still tend to be smaller than you assuming you buy a settler, get a free settler from Liberty, and chop through a settler or two. Only if you focus on going super-tall will they be larger than you.
On anything above Prince, you risk that they may very well expand faster than you, even if you are trying. On King, you may out-expand them, but it won't be by as much as Prince. On Emperor, they will likely be roughly the same size or bigger. Above that, it gets ugly.
Of course, it all depends on who the other civ is. If it's just you and Egypt on a Huge map, you may expand quicker than them by far even on Emperor. If it's just you and Hiawatha, though... well, he's probably going to have twice the cities you do on Emperor, and on Deity he may control vast amounts of space.