Apologies that I couldn't find a better comparison for the Houses of Parliament, turns out there aren't many building like it. Anyway this is what I think...
Battle one - Houses of Parliament because they are so beautiful
Battle two - Tower Bridge because it is more historical than Golden Gate Bridge, and it opens. It was a close one though, Golden Gate Bridge is also magnificent.
Battle three - The Capitol Building - much more 'grand', IMO. I have never liked St. Pauls and I find the colour of it depressing.
Battle four - Piccadilly Circus because it is more elegant and there are better shops. I hates Times Square, it is so overrated and a tourist trap.
Battle five - I actually prefer Angel of the North because I find Statue of Liberty to be overrated.
Battle six - Mount Rushmore because Stonehenge is the most overrated landmark in the world. I went there expecting something amazing and it was literally just a pile of rocks.
Battle seven - The Lake District because I prefer the scenery, although Grand Canyon is also impressive.
Battle eight - Central Park, no question. London has better parks overall and Central Park can be too crowded, but still, none of London's parks come close.
Battle nine - I prefer the Shard, it is so beautiful, especially in the sun.
Battle ten - The O2 is better looking, IMO, although I've never actually been to MSG, I've only seen it from the outside.
Battle eleven - Buckingham Palace is nicer.
Battle twelve - Trafalgar Square is beautiful and Nelson's Column is more interesting.
Battle thirteen - Very close but I think the London bus has the edge, it is far more quirky.
Overall - it is really close but the UK wins due to its history and heritage.
I only put some of the most famous landmarks here. Really the most beautiful castles and building in the UK are outside of London and not so well known.