I would be worried about London, I live here. It is fairly regular to hear incidents of phone snatching or watch snatching whilst out and about. Obviously certain areas are a little safer than others but it has happened in nicer areas too and in broad daylight. These guys are fast, they come on mopeds and can carry knives. Not trying to scare you but it is common in London with these incidents happening. I no longer use my phone out and about it stays in my pocket and if I need to use it I quickly pop into a coffee shop.
I’m not a New Yorker but I don’t think I’ve heard anything about watch or phone snatching. I haven’t heard of anything like this about any other big cities, but I’m not a local so am sure there are a few of these incidents.
I feel like jewellery is a little safer, people don’t necessarily know the value unless it is a popular brand and unlike certain watch brands you lose a lot of value with resale.
