ftp might have some annoying limitations and features, but on the speed issue you won't actually find anything that is significantly faster when you are talking about just copying a file from one location to another

(the same doesn't apply when you are doing something like syncing a set of changing files, when of course things like rsync that do diffs are far faster)

If the client has something like an ADSL line with low upstream speeds, they might be running into the problem of the upstream bandwidth being saturated for long periods which then breaks everything on the line that is trying to use TCP. When that happens you really need a way of throttling the upload speed to keep it from fully filling the line.