I've called both numbers a few times over recent years.
999 for domestic assault of a neighbour, I could see into their house and there was hitting and throwing of stuff, I was worried for the lady's safety. Had to do this a couple of times.
999 for an ambulance for a lady who had fallen and bumped her leg, she was struggling to get up and bleeding from a couple of injuries, plus she was elderly.
999 after we were in an accident on the motorway, a lorry shed some of its load. Big aluminium sheets flying off right at us, another lady stopped as a witness, the gentleman was being difficult about insurance details, and I knew the debris on the motorway was a hazard.
999 a few times during pregnancy as I had bowel blockages that were incredibly painful and needed enemas to ensure I didn't get infection in my body elsewhere.
101 to report domestic abuse and harassment since I had left, then again when I moved area to keep local police updated about my worries of being found, I wanted to be sure my address was on rapid response in case my ex did turn up.
I had an ambulance called for me a few months ago on 999, I'd fallen and sprained my ankle, but it hurt a lot and I was worried it might be broken. I couldn't get up either, due to my disability, my hips were going into spasm if I tried anything but lying down.
I've called 101 various times when I lived next to a pub, fighting/shagging/defacating in the garden. Once for a drunk old man who had collapsed mid-winter and unconscious.
Probably the least appropriate time I called was a 999 call when my DD ran off in a busy town centre. I was on my stick rather than in a mobility scooter and she was four. She had behavioural issues and doesn't recognise danger, and she was running toward the busy road at the other side. Fortunately the police station was just over the road she was running around to, and the collected her and brought her back to me, then got us into a taxi to get home safely as DD was having a bit of a meltdown. At the time, making that call was all I could think of to keep her safe.
She was also brought home in the middle of the night by the police after circumnavigating all my extra locks and hidden keys. She knocked on random person's door because she was lost and wanted to come home. Boy was I glad that the person called the police.