You have researched and discovered the answer to this already with your A/B testing. I would conclude that there is no benefit from the left location to the right (depending on length of A/B test and the amount of eyeballs that have seen both layouts).
If you are still uncertain about this, do some quick usability testing. Write a scenario question along the lines of:
“You and a partner are planning a weekend away to the White Peak in
Derbyshire next weekend. Find somewhere to stay that will sleep you
both for 2 nights.”
This is a non-leading question that gives the user testers some scope to explore ways in which to book the location. You have not explicitly mentioned any of the words that are in the widget to give the game away. It will then be your job to check for any hesitations or issues in locating and using the widget. Try it out on at least 5 people.
I would probably refer to this as a booking widget rather than quick search. Search is normally top right, like on StackExchange, where it is expected to be found by the user. In this case, the user is required to choose a location and date for a booking, and the actions are self contained, so this has the characteristics of a widget.
