Yes, I agree a dedicated server is always better than shared environment, but defeat your own argument against Magento being slow when you suggest a dedi.

If your client is serious about your online business, don’t use shared hosting but get a proper dedicated server instead. I’d also highly recommend seeing a Magento specialized hosting company, they’re worth the extra buck.

via Magento – Blog – Magento Performance: Myth vs. Reality – eCommerce Software for Growth.