We are moving our FTP server to a data center, which will have a 50Mb pipe to the internet. Will our customers see a an increase in file upload speed once we have moved? What is unclear to me is if our clients are uploading data from their prospective connection then how will our 50Mb connection be relevant?
It all depends on several factors:
It entirely depends how congested your current connection was. If transfers were maxing the connection out fairly regularly, then yes the extra bandwidth will be noticable, but if they were not, then no there will be no noticable difference.
Think of it this way.
Say you have a 10 MB connection now, and each customer has a 1 MB connection.
If you have 10 customers all using the connection you will be maxed out and each customer will be able to use all of their bandwidth. If you have 20 customers using your 10 MB connection then each customer, in theory, will only have .5 MB available to them.
Obviously, that's a pretty simplified answer, but it should explain things for you.
It depends on what your original pipe speed was, how many concurrent sessions you have coming into your pipe (ie- were you pegged with your original connection) and, yes, what their pipe speeds are. As in anything your bottleneck will be the slowest pipe (or worst route if there's big problems somewhere). In general your customers who are on slower pipes than your original connection won't notice much, if any, improvement. Others with bigger pipes might notice some slight improvement.