It's already been said in different ways, but I feel compelled to say that London for 3 or 4 days at most just feels crazy to me. You could spend 3 or 4 days just on palaces, just on historical sites, just on markets, just on museums, just on parks, and another 3-4 just on art museums. So I think unlike many cities, regardless of your interests, you would find more than 3 or 4 days worth. If you absolutely hate cities, then the day trips also are good; you could do Cambridge, Oxford, Canterbury, Windsor, Bath, or Stonehenge.
Since you haven't been to either, I suggest that you pencil in 7 nights in London and 7 nights in Paris. Then when you have purchased your guidebooks, or borrowed recent ones from the library, start charting out the big things you want to do each half day. This will probably tell you how many nights in each one, but if you have 12 in one city and 2 in the other, I wouldn't bother with the one with very few nights.
London is very dispersed, but the tube/underground system is huge, so there's no one right answer, or even two or three right answers, for London. You will be able to get around. Paris also has a very robust transit system, although veteran travelers often have some preference for staying in the single-district arrondissements (districts), which are closest to the river. After you have your target sites you want to see, look at booking.com to see what hotels might be central to those. You don't have to book through them.
I love both cities, which are quite different in tone from each other.