I know this question asks specifically about performance implications, and there are good answers here already, but I think it would be remiss to not mention a topic that hasn't been broached yet when talking about multi-tenant solutions: security.
When you hold data for multiple customers in a single database, you have to be extremely careful when it comes to security, not only in the database itself, but in the application(s) as well. Generally speaking, one customer should never be able to see another customer's data. I don't know your business, but this is usually the case.
When architecting an application, creating security boundaries is desirable, so that
if when your team happens to make a small mistake, there's already a built-in fallback to prevent Bad Things from happening. A database is one type of security boundary.
This separation (a business requirement, which may or may not exist) needs to be balanced with your plan to manage the data, performance, etc., though security requirements can (and should) trump everything else if it's deemed important enough by the business.
Yes, it sounds like there's an echo in here, but it really does depend on your exact situation to make the best decision. All we can do is give you ideas to help you reach that conclusion.