For me it depends on the usecase. For a payment oriented use I prefer on a phone because of ease of use and mobility. For store of value use I prefer a desktop application with a hardware wallet because of security.
At first sight a browser extension seems to be the worst of both worlds, low mobility and low security. Of course it is not necessarily low security, but that is based on my personal impression of browser extensions in general.
Just noticed OP explicitly mentions Lightning, in that case it would be phone.