I have an ipad2, and I have this keyboard case: http://www.logitech.com/en-us/1222/8213
Will the "new ipad" fit nicely into this case, physically? Or, if I get one of the new ipads, will I need to get a keyboard case specifically "for new ipad"?
Yes, it fits. I bought the iPad 2 case and it fits my third gen iPad...$20 cheaper too :)
The latest generation iPad is slightly thicker then the iPad 2.
The iPad "2" is 0.34" (8.6 mm) depth
Otherwise they are precisely the same width/height.
While I don't have the case/keyboard you mentioned, it looks like it may fit in there. If the case has a solid nook for the iPad to fit into, it likely will get (noticably) tighter - but it entirely depends on how much gap is provided. Obviously since the new iPad hasn't been physically sold yet, there wouldn't be a way to actually test - other then measure with something like a micrometer.
Answering my own question from the new iPad at the Apple Store. Definitively yes.