In most situations, Web Access is not going to be faster or more responsive than the Windows client.  The thick client has the advantage of talking directly to the Laserfiche server.  Given how the applications work, one scenario where Web Access might have an advantage is low bandwidth and low processing power on the client machine.  If you add in Web Accelerator, Web Access also benefits when there are image cache hits (i.e. different users looking at the same pages).

But in general, you aren't choosing one solution over the other because it's the fastest.  You are choosing one over the other for a variety of deployment or integration reasons, and then making sure it's fast enough.  Both applications should be fast enough.