I would do one city as there is so much to see and do in each city. Plus you have to take into account getting from London to Paris on the train which takes time and you will take most of the day doing that. I think if you go to both cities in only 8 days you will again feel short changed. And as you already know there are tons of day trips to take from both Paris and London. In order to make a decision on which city, read the RS guide books and other guide books, look at the YouTube Videos and look at the RS scrapbooks on this fourm.
I loved going to Windsor Castle, Hampton court, taking the London Walks during the day walks and the pub walks, spending time in the Tower of London, Churchill War Rooms, the Victoria and Albert Musuem, British Museum, taking the boat ride up the Thames to Greenwich, going to pubs, seeing the food hall at Harrods, seeing a play, going to the National Gallery of Art and the National Portrait Gallery. I have been to London several times and still have not seen it all. This year I am going for two weeks and am going to go to all the places I have not been to yet and a few I have been to! I am going to a classical concert at St Martins in the Field church and a play and taking day trips to see Downton Abbey and a day trip to Kew Gardens and a day trip to the Cotswolds. More London walks and never been to the Musuem of London or the National History Museum which are on my list for this visit.
As for Paris, I have also been there several times and am planning to go there in the near future. I love seeing the same things in Paris over and over and need to go to new places in Paris. I loved my day to Versailles and walking the extensive grounds and gardens and seeing the palace. My favorite art museums are in Paris along with the best dining. The list goes on and on as to what to see and do in Paris including a day trip to Monet's Gardens!
So I thinking splitting the days when you have only 8 days would be as you put it short changing yourselves.
I hope my comments find helpful. Now you just need to do what would be best for you. Have a great trip and safe travels!