Best way to do this for SEO

I have a site example.com that has been live for some time now, the SEO isn't that great, but it's ok, to be honest it's not been a focus as it's been in a niche that doesn't need great SEO.

I'm currently re-building this site on a subdomain, as we are moving to a sector, or focusing more on a sector that requires powerful SEO.

The site will have the same content, it will just look, and perform much much better.

My question is, when I put the site live, do I keep it on something.example.com, and let the visitors on example.com choose whether to use something.example.com (by using some sort of announcement message) or do I just push the rebuilt site directly on to the main domain?

Any advice welcomed.