Time machine backups are extremely slow after Mavericks upgrade. Why is this happening?

I can suggest a few things to try but I am yet to see a solution.. I am not prepared to move to Mavericks until a couple of revisions fix the beta standard of some of these things. TM in particular seems to have badly suffered.

Are you using wireless? Especially double hop wireless with the TC as the extend.. don't!!

Use ethernet direct to the TC and turn off wireless.. see if that helps.

Otherwise I reckon until Apple get an update use a local usb disk plugged into the computer and don't try and use TM to network drive. Or if you still want to use the network drive use something like CCC which should be fine under Mavericks since it is a much more robust software. (without lots of bells and whistles.. but functional).