publishing on a server is mainly for sharing purposes.
It can improve performances because servers are, mot of the time, more powerfull than Desk/Laptops.
In our company, standard users have 2cores - 4 Gb RAM PCs, the server is 8 core - 64 Gb RAM.
We use datasources with large extracts (25-30 Gb), and queries are faster on published datasources.
It also depends on your network performance/availabilty.
I won't be able to tell you which one is faster because it depends on various factors like data size, dashboard complexity, generated query complexity etc. but I can tell you that we've seen (and aware of) non-trivial performance differences between these two approaches due to extra abstraction layer added by .tds/.tdsx.
Out general advice - go with published extract just because they are reusable so they'll put less stress on Server during refreshes plus will provide extra caching opportunities for all dependent workbooks.