I want to decide on the domain name for my software company. Let's say it's called "Big Example Software".

When someone types "Big Example Software" I want to be the number one result in search engines. I currently have both bigexamplesoftware.com and bigexample.software. I think prefer the .software domain extension as it looks neater, but will it harm my efforts to be the number one result? Any other downsides to it?

Unfortunately the equivalent of bigexample.com is taken, as that'd be the best of both worlds.