Shared hosting means that you’d share a disc space with other users. As a result you end up with a slow website that is constantly unvailable and vulnerable to security attacks. IT WILL INEVITABLY AFFECT YOUR RANKING IN A BAD WAY.
VPS, on the other hand, is isolated from any other websites. It means that you get good speed of your website , less down time and good servicing. THESE ARE VERY IMPORTANT FACTORS FOR HIGHER RANKING.
Good server provides good speed and less down time which indirectly helps in SEO
When choosing a VPS hosting provider for SEO
make sure that you choose a company that has years of experience, good support, clear SLAs and offers managed hosting. I recommend you to check out AdvancedHosting