Hi BillEssley, I don't know if budget is your constraint, but assuming that it isn't I would go for a dedicated server but only after understanding my requirements. If 16 GB RAM is what you are looking for I would go with an SSD and not HDD for the simple reason that I prefer flash storage without many moving parts.
Performance-wise, dedicated wins because unlike VPS it won't share resources, and secondly, as someone rightly mentioned, what is your exact hosting requirement because both machines are good in their own way. A VPS with 16GB RAM will work wonders if you are hosting a new site that is functioning on VMs that have adequate (or should I say limited) performance levels. On the other hand, the dedicated server with 16GB RAM and other resources will boost your website's performance.