I've pondered this one, and I think I can truthfully say that I would hand them in. Mainly because often watches (especially good ones) can have alot of sentimental value, having been given as special birthday presents etc. Having an
insurance cash payout doesn't compensate for the sense of loss of a cherished present or family heirloom. But to be honest, if the person who has lost the item has had an
insurance payout, having the item returned to them could really cause them problems if the payout has been spent and then has to be repaid.
If I found a tenner or twenty quid lying around, I'd probably keep it after having a look round to see if anyone was obviously looking for it, if it was in a shop I'd leave my contact details in case anyone went back to ask about it. But any more than that and I think I'd hand it in. For some people losing fifty quid is nothing, but for others it could be a major disaster.
Last year I lost my house keys in town, I knew they had to be either inside the co-op or on the pavement outside, got home and realised, drove straight back and asked in the co-op but no-one had reported them. I thought it was a bit of a long shot but I went to the police station and asked on the off chance. Someone from a nearby village had just phoned up and had reported finding them and that they had them at their house. I was so relieved and thankful but the police wouldn't give me the person's name and address so that I could go and get them, I had to wait at the police station for the police to go and pick them up and bring them to me. I was disappointed not to be able to thank the person directly.