Been to both cities repeatedly, and it's really a question of, what do you love? Paris is special if you get a nice hotel. There's loads of dives there you really don't want to stay in, but when it's good, it's GREAT. Food is usually excellent, (toilets not so much...) tourist locations aplenty... Personally I love the Mont Martre area and the stunning statue of the Archangel Michael in the Sacre Coeur, the giant flea/antiques-market, and if you have a chance to hop over to Versailles I'll be super-jealous because I never managed to go... I went down into the bone-filled catacombs, saw Napoleon's tomb and visited Jim Morrison at Pere Lachaise. (I'm a bit morbid, granted.
). The Champs d'Elysee isn't want it used to be, but there are so many nice places... The Messy Nessy Chic people have a lovely online guide to Paris' top hidden-yet-lovely spots, that might be worth a google or add on facebook. Did you know the Louvre still has the living quarters intact of one of their kings? (Napoleon the 3rd, off the top of my head) I can't believe I missed that, but it seems like most people don't know its even there. Never went up the Eiffel Tower, (Hights and queue's... Nah!) but I can recommend taking a dinnercruise on the Seine. Last time I was there was because Stephen King was having a talk at the Grand Rex, and we had a tiny little appartment across the street from a chocolate shop.... It was a slice of heaven, and since I've turned our own place upside-down to resemble it more. (Still nowhere close, I'm too messy. But I did steal the colour scheme and got a Nespresso like the one they had. One weekend, and I was hooked on Volluto.
).
London however... I can stay in Paris for a week and not be bored a moment. Plenty of museums and the like to keep me occupied, and just walking the streets, there's enough to fill the senses. London's more my cup of tea though, as a kid I wanted to go live there some day...
For one thing I speak the language, so that makes me more comfortable. French is still just waving arms and legs around and hoping they understand me; if you speak french, that might not be an issue. I'm a royalist, love victoriana, english gothic novels, the classics, and ghoststories. (Is Foley's still a thing?). The tower, Buckingham Palace, the closeness of Windsor, all the tourist-traps I love so well... Still want to visit Highgate someday (yeah, noticing a theme I guess, but I'm an amateur photographer and I'd go NUTS there), oh, Forbidden Planet, Selfridges all that lovely shopping... My husband's company treated its employees and their spouses to a weekend, had a dinnercruise on the Thames, went to We Will Rock You... No idea how to arrange that as they did it, but it was lovely going out to the theatre there. Had a breathtaking time in Windsor at the castle, having tea in the library over at Oakley Court (Where loads of Hammer horror was filmed, as well as the Rockey Horror Picture Show)... When I visited Buckingham Palace and went in through the ambassador's entrance, i quietly wept, haha. Husband had to drag me out of the throne room.
Enough to see and do, in either place, really... St. Paul's, Tower Bridge, the museums, the Eye, the lovely parks... And the massive amounts of shopping that need to be done.
Honestly? I think you'll have a wonderful time in either city. So do tackle them both.