Don't have a comparison but I suspect the A14, being a cut down sister chip to the M1 effectively, is probably going to be kinder on battery life at the expense of performance. The air also seems to have a (very) marginally larger battery from what I can tell.
That said, the ProMotion display is likely to be more power efficient than the Air's 60hz display, because the Pro is "up to 120hz" meaning it can drop down to lower refresh rates if you're doing tasks like reading a book where the page content doesn't need to update as frequently.
All in all, you're likely to get more or less the same battery performance from both - perhaps with the Air taking a slight lead due to the lower clocked A14 in general tasks.