Hi.
_"Lithium Polymer does not equal Lithium Ion"._
Certainly not! They are an improvement. But the question here is whether their charging and use characteristics are the same, and they are.
_"Do a web search, there's lots of info out there..._"
I did, and found that there is a lot of mistaken and/or garbled information being put out, even here on the Apple forums!
Interestingly battery technology in the Li-ion field is changing rapidly - every few months, and the total lifetime capacity of the latest series of batteries isn't known yet. They may well work "fine" after 3 or 4 years, or maybe not. Probably not.
Still, they have similar characteristics with respect to charging. "Regularly exercising" the Li-ion battery is not necessary nor even desirable, EXCEPT to keep the battery indicator/software functioning reasonably accurately on the iPhone itself. This is where I choose to follow the battery manufacturers specifications, notes, cautions and recommendation versus third or fourth hand information from general owners of the device that uses it. I think that makes a certain amount of sense, wouldn't you agree?
For example, it's commonly stated (here) that iPhone users should "discharge their iPhone all the way to zero at least once a month to keep the battery healthy."
What does the battery manufacturer say about this? They recommend a full discharge every 30 charge cycles, which isn't anywhere near 30 days depending on the use level! They go on to say that the battery is quite happy in a mostly charged state - but that the battery indicator will become increasingly inaccurate over time if the discharge is not performed periodically.
According to the battery manufacturer, there is no "memory" with Li-ion, nor are long "priming" charges necessary. (This is why it's OK to leave it on the charger semi-permanently) - any battery is degraded by a full discharge condition. This is especially true with lead-acid type batteries. Oh, they will charge up again - but they will never quite be the same. Trolling or "boat" batteries are designed around this problem.
The point I quoted about Ni-cads is an important one - lots of research by industry (people who use radios/cells and other rechargeables) found that light use over time and constant charging counterproductive - when the item was eventually called upon for a full duty cycle, they failed right away. Oops. Li-ion are advertised as immune from this problem.
For the folks who are complaining about the expense of replacement batteries down the road, consider the value of rechargeable packs - how much are those 4-packs of "AAA" cells right now? 5 bucks? That would add up awfully quick.