Li-ion mobile phone batteries are lighter and have no memory effect meaning you can part charge them with no disadvantages.
Unused- Lithium mobile phone batteries will lose only 15% of their charge in a month whereas unused NiMh batteries will lose 50%.
Fully charge your new mobile phone battery when you receive it for at least 16 hours. Try and use the battery full to empty the first couple of times.
Lithium Polymer mobile phone batteries were developed from Li-ion batteries. L-Po cells can take more capacity in the same physical volume.
Higher capacity L-Po mobile phone batteries mean more talk time, more standby time and more time between charges. The same charger can be used. As an upgrade it is well worth while -- substantial benefit for moderate expenditure.