[Galaxy Note II Accessories] ttabbal:
There seem to be a few misunderstandings here regarding batteries and chargers.

1) The charge rate, when the battery is in the phone, is controlled BY the phone. The charger itself just supplies regulated power to the phone. How much current is put into the battery at any given time is up to the phone, which is why kernels can do things like fast charge, it's controlled by the kernel. Now, the reason the battery charges faster when using the stock charger vs. something lower current or a computer is simple. The phone can detect what it's connected to within some limitations. It sounds like our phone can also sense the incoming voltage levels and back off if the supply becomes unstable.

2) Using the stock 2A charger is "harder" on the battery than a lower current charger. Not true, at least not within any margin of error you will be able to detect without specialized equipment. Lipo batteries are generally built to charge/discharge at 1C. C in this case stands for capacity. So our 3100mah batteries can charge at 3.1Amp and be within safety margin. So the 2Amp charger the phone comes with is perfectly fine for the battery. Without seeing a datasheet for the battery from Samsung, that's a good guess. And again, the phone controls the charge current based on a number of parameters. You could connect the phone to a 5V supply capable of 100Amp and it will still only use what it needs.

3) The percentage readout on the phone screen is a GUESS. Don't pay it too much attention. For this same reason, evaluating 3rd party batteries based on phone runtime etc is not useful. To validate the battery capacity with any accuracy requires a test setup discharging the battery through a known load and measuring how long it takes to get to a cutoff voltage. I've done some of these tests myself on stock and 3rd party batteries. In general, the OEM batteries are always at or above spec, the 3rd party battery manufacturers lie. Often by upward of 20%. Even the high $ batteries. Keep that in mind when shopping if you want extras or extended batteries.

4) Interrupting the charge cycle is bad. Nope. It's fine. On this same line of thought, full cycles ARE bad. Don't do it. Don't think too much about it either though. Just plug it in when convenient. Or set it on the wireless charger if you've installed one. Generally speaking, they actually don't like to be charged to 100% either. Keeping it at 20%-80% is actually best for the longevity of the battery cell itself. In practice, you will probably have a new phone before any of this is actually noticeable. :D

The OP sounds like they are talking about a stand-alone charger, where the battery is not in the phone. Those will vary wildly in quality and capability, particularly from ebay. They are probably cheap POS devices. Not that that's really a bad thing, just know about it. It's probably a very low charge rate device, perhaps even down to 100ma or so. That would take forever to charge our larger batteries. As for if there is a better one, probably. If Samsung makes one, it will probably charge faster than the phone with the provided charger plug as there would be no load from the phone using power. Of course, it will cost a lot more as well. Look for devices that at least claim they will charge at 2Amp or so. In practice, they will probably be a lot lower, but your chances are improved. Not many people will break out an ammeter and check, after all.