Here are a few batteries from the iPod Video and classics.
Arranged from left to right, in the order of good to bad:
Model 616-0230. Li-on, This blue battery is the best in terms of capacity and reliability, OEM, manufactured by SANYO.
Model 616-0229, Li-on, can be identified by the yellow kapton tape insulation. OEM.
Model 616-0392, Li-on, 2.04whr, all black wrapping, OEM, a little thinner than the above two, so a little less capacity?
Model 616-0412, Li-polymer, OEM, marking: 2.04whr, 550whr, capacity is OK however tends to swell when over discharged. May have poor protection circuit implemented, some battery getting really warm during charge, could be hazardous as the battery in iPOD nano 1st, Gen. I am surprised that Apple didn’t recall this.
Model 616-0227, Li-polymer, OEM, seems to be the same battery as above with different model numbers.
For 616-0230, Li-polymer, non-OEM, marked as 650mAh but definitely over rated, poor performance even when new.
Conclusion: Li-on battery is more reliable than li-polymer battery, choose li-on battery if you can, avoid non-OEM batteries that is over rated in capacity.