In the UK, bicycles are supposed to follow the same road laws as other users regarding traffic lights etc so there's little benefit to using one over a moped other than running costs (tax/insurance etc).
Moped theft here is very high and (normal) bicycle theft is ridiculous - I've had 2 £1000+ mountain bikes stolen. My current cycle never leaves my sight when I take it out of the shed, which means I can't nip in to town with it. I know that the toe-rags will be off with it in seconds.
I'd love to put an electric rear hub on it but that just makes it more attractive to thieves.
That's unfortunate. I've heard about this issue, which is supposed to be especially acute in London.
Here in Chicago, it couldn't be more different. I have started riding my collection of old 3 speed "english racers", and these seem to be positively theft proof, I only occasionally lock one, in particularly exposed areas, but mostly rely on the general laziness of thieves, along with the relatively poor cosmetic condition of the paint to protect them. One method that seems to work, I'll flip the bike over and leave it upside down, on it's seat and handlebars, an old trick we learned as kids to prevent some other kid from jumping on your bike and riding away faster than you could run him down from behind.
Mopeds have never been officially recognized locally, they don't exist legally and this makes riding one quite awkward, in my view. They tend to be available used without titles, while the police want to look at them as motorcycles, which, like scooters, require registration.
Bicycles, on the other hand, are just generally ignored. No registration, no license, no insurance requirements, no restrictions, and this seems to apply equally to those equipped with the 66cc china "whizzer" engines, which can be had in kit form for about $120, complete. Cops just look the other way. We have laws on the books that let a bicyclist go through stop signs, and red lights under certain conditions. It's quite infuriating to the cage drivers. They will curse the first few times I re-pass them while they wait at the traffic light queus, but by the third or 4th time, they seem to accept it. I try to ride respectfully and safely. I'm in my 60s.