Bottom line: pick by scale and trip length — choose London for iconic landmarks, free world-class museums and big-city energy; choose Amsterdam for a compact, bikeable, 3–4-day-friendly charm. London covers over 1,500 km² (plan 6–7 days); its biggest draw is free national museums (British Museum, National Gallery, Tate Modern, Natural History Museum, V&A) plus a diverse food scene (Borough Market, Brick Lane; street food £8–14, set lunches £15–22). Amsterdam's historic core is crossable by bike in ~20 minutes; the canal ring is a UNESCO World Heritage Site. Must-sees: Rijksmuseum, Van Gogh Museum and Anne Frank House (book weeks ahead in peak season). Eurostar links the two directly — St Pancras to Amsterdam Centraal in about 3h40 — so you can combine both.