I have several old Lincolns and Indian cents in various grades of BU and Proof and was wondering if there was any difference between the grading companies in the way that they grade copper coins. Any thoughts welcome.
It would depend on the grades that you expect to get. If lower grade uncs, I'd use ANACS. They are running a special right now.
I agree with Treashunt, but rememebr that the cheaper the grading, the less "respected" it is, so your MS64 RD Indian might only sell for the price of the same date in a PCGS but graded MS64 BN. If you have any varieties, ANACS is 100% the way to go, but if you have anything more valuable or that you plan on reselling later then you might want to head over to NGC or even PCGS.
If you want to get the most for your coin, go with PCGS. You might take some grading lumps from them, depending upon whether they in a "soft" or "hard" grading cycle, but more people seem to be drawn to them.
The top three have been given to you but the best one, in my opinion, is your own! Unless, of course, you need the cash.