I do believe, if I remember right, that I did delete the cache etc. before I saw a big improvement (I ran the latest version of Onyx). So this sounds like good advice from dominic23. But I do want to reiterate, I had horrible Internet speed... on pretty much all networks, including outside our home... when running Yosemite. But in El Capitan, it's consistently at the 9 mbs rate (which, for where we are, is about as fast as it will get).
Something else that seemed to be a huge help was making sure to NOT be running Dropbox or Google Drive. Even when you're not uploading anything. They both seem to place a crazy drag on things. Also, check to make sure the slowdown isn't due to other updates being downloaded or pics or music being synced to iCloud... a distant possibility, but possible nonetheless.
One other thing... I did notice, during the Yosemite issues, that connecting my computer to the network seemed to slow all others. Whatever it was was definitely buried somewhere in the System files, I'm guessing, but not something inherent to the core. More likely... something gone wrong with the local administration of everything... like a specific setting or, as dominic23 says, a cache that's gone wrong.
All this just to say... I don't *think* the problem is El Capitan itself. It sounds like it's something else. Said just so you can start looking down a different path for solutions.
From this link, some suggestions: http://www.gottabemobile.com/2015/10/02/common-os-x-el-capitan-problems-fixes/
For the most part the OS X El Capitan WiFi problems are small and less likely than on OS X Yosemite thanks to a major change by Apple, but there are still some problems you may run into.
If you need to fix slow WiFi on OS X El Capitan, you may need to restart your router and modem, unplug them for about 30 seconds to a minute. If this doesn’t fix it you can try turning your WiFi off on your Mac. Click on the WiFi icon and then Turn WiFi off. After a minute turn it back on. This can fix many problems.
Other potential fixes including clicking on Open Network Preferences and then on Advanced to change the order your computer should connect to, options to delete a WiFi network and more. Sometimes deleting a connection and re-adding it will fix the issue.