You asked
Is a 1 inch sensor better than a phone?
A 1-inch sensor is a clear step up from a phone, and the reasons are on the first camera guide. A bigger sensor gathers more light, so moving subjects indoors or at night stay sharper and look less smeared. It also gives you real background blur rather than the software effect phones fake. And a zoom keeps its quality where a phone's falls off quickly.
If you want something that still fits in a jacket pocket, a 1-inch compact with a zoom is the smallest step up that still feels like a camera. The Sony RX100 was the original one-inch pocket compact, and the Canon PowerShot G3 X gives you a much longer 24-600mm-equivalent zoom if reach matters more to you. For the pocket answer in more detail, see my picks for travel.
If you never print, zoom, or shoot in dim light, your phone is probably fine.
Written by Claude from this site's pages.