google chrome is using your personal data to show the rankings of your website........................so first creal all cookies and data the search and disable the customization..............search option.............
There are different in ranking when you use different web browser for searching. I've my website ranked 1st in firefox but later then i notice it ranked 4th in internet explorer and i believe this has to do with your website preference in cookie like the reply above.
yes, crome is from google, and it is personalized for the user by google,,so it will be different when you search using your personal profile..
When you search from Google using Chrome or Firefox, make sure you are - Logged out from google account - Disable customization (Once you hit search button, you will see "Web History" at top right section in Google search page where you can disable this) Just follow the above steps and you will get similar results from any search engine.