Charging
Despite the significant increase in battery capacity, Apple continues to ship the new iPad with the same 10W USB power adapter as the previous two models. You can charge the iPad via a Mac/PC USB port that implements the USB charging spec, however doing so will take a minor eternity to fully charge the tablet. Just as before, the new iPad will not charge off of a USB port if the tablet is awake; it will only charge when locked/asleep. The convenience of having a USB based charger is evident, but you'll want to stick with the 10W adapter to actually charge the iPad.
Charging the larger battery does take longer. If we measure from a completely dead state to when the iPad indicates that it's fully charged the increase in time is approximately 50%, from 4 hours with the iPad 2 to 6 hours with the new iPad. ASUS' Transformer Prime, by comparison, requires only 2.5 hours as it ships with an 18W charger. And no, you can't use ASUS' charger to speed up charge times on the new iPad - when connected, the TF Prime charger will only supply 9W to the iPad.
The story doesn't end there however. While the iPad 2 will draw 0W after its 4 hour charge cycle is complete, the new iPad will continue to draw around 3W after it claims to be fully charged. This will continue for roughly another hour at which point the power adapter will draw anywhere from 0.1 - 0.6W.
Note that when running at full brightness and with a heavy GPU load (e.g. Infinity Blade 2), the power adapter can't supply enough to keep the iPad charged and drive the display/internal components.
There's no good solution here other than for Apple to start shipping the iPad with a higher wattage power adapter. I do believe faster charge times are going to be necessary if Apple is keen on sticking with this larger battery, not to mention the usage issues of not being able to maintain charge equilibrium under load.