We recommend that you wait on moving servers until after we optimize your website. Even if your site is very large, there are ways to optimize it that can help deliver better performance regardless of your host.
However, larger sites with lots of content and media are likely to be a bit slower than smaller, more lightweight sites. Once we optimize your WordPress website, our team can work with you to determine if you could benefit from a faster hosting plan, platform or even a VPS or dedicated server.