It is not easy to say one way or the other because we don't know the parameters that you face.  One easy metric would be memory size.  If your problem won't fit in the smaller 480 memory footprint, then you should go with the C1060.  However, if it will fit in the footprint, then the 480s will probably give you more speed (since they are Fermi-based and the C1060 is not Fermi-based).  

Also, the C1060 typically comes with better support and warranty than the 480s, so if those parameters are important, they may influence your decision.

Also, the C1060 will be available "new" on the market for much longer than the 480s.  They GeForce lines are typically not shipped more than 2 years or so as they get replaced by newer lines.  But since commercial entities are building products with the C1060s in them, the Tesla lines have promised to keep the lines going for a longer period of time.

Hope this helps and good luck!