What would you choose as the top 5 activities/attractions in both London and Paris for teenage girls?

A very quick, not complete answer, based on my daughter's experience:

Camden Market
London theatre
Abbey Road studios (of Beatles fame, at least for my daughter, along with the London Beatles walk)

Centre Pompidou
Paris shopping - Tati, vintage stores, Porte de Montreuil flea market

Our girls' favorites were the Tower of London and Versailles. They were 13 and 16 at the time. They were intimidated by the thought of shopping in Paris, but they did want to go to Burberry in London. That was 2004; it may no longer be popular!

Can't speak about London yet but my top 5 Paris sights with teen girls would be:

1. The Eiffel Tower (it's a gimme right?)
2. Mussee D'Orsay (even teens can appreciate Degas' ballerinas!)
3. SHOPPING! Sorry to shout but we are talking about the shopping Mecca here! I suggest checking out perfume & cosmetics they can't get at home. Le Bon Marche, Galleries Lafayette, Pritemps and the flea markets are fun. There are also some stores that sell used designer labels. I can't give you addresses but I think if you google it you may find some. And of course The Champs
4. Seine river cruise at night
5. Versailles (if you have the time)

London:
Cabinet War Rooms
St. Martin in the Fields cafe and brass rubbings
Tower of London tour
Ghost tour-London Walks
Barbican Theatre Shakespeare
Paris:
Markets
Window shopping anywhere
Jardins du Luxembourg
Montmarte - walking around
D'Orsay

There are free fashion shows at the Department Stores such as Galleries Lafayette in Paris - they are really fun for teen girls. I believe you need to reserve in advance, which you can do from your hotel once you get there. We also went to a flea market while we were there, which was a big hit. Eiffel Tower despite being so touristy is really fun. They also loved all the pastry shops.

See what will be on display at the Victoria and Albert Museum in London -- my teen girl really loved that museum. Other big hits were the Tower of London, and a rowboat ride at Regent's Park. It was a welcome break from touring and walking around. The kids loved rowing and there is a gorgeous little lakeside cafe for a cold drink or ice cream.

An excursion to Hampton Court is fun for teens, with its real hedgerow maze and interesting castle tour. Familytravelforum.com might be a helpful website for you as it contains suggestions and travel tips for teens as well as kids.

what I think her top 5 in London were:

theatre (especially Shakespeare)

shopping (especially Liberty, vintage shops, and of course, Top Shop)

markets (she LOVED Borough food market, and also liked Portobello. She thought that the atmosphere at Camden was "forced" although she found things to buy

the Crown Jewels/Tower of London

the Turners in the Tate Britain and the National Gallery