GPU rendering speed for 3D FlasCC games/apps is likely to be similar to C++ apps for obvious reasons - the actual rendering takes place on the GPU. Flash includes a cross-platfrom shader language (AGAL) to describe GPU kernels (programs run per pixel on the GPU).
CPU/computing speeds however at best reaches 15% the speed of MS VC++ on Windows (tested with a simple encryption function operating on an array of bytes). Some benchmarks for the latest FlasCC are available here, that compare a set of C++ programs running as an EXE and in Flash Player.
This essentially comes down to:
Anything you can move to the GPU can possibly be done close to native speeds. This includes rendering, lighting, mip-mapping, and to some extent physics operations (depends on the library)
Anything still done on the CPU will be a few times slower than C++, so don't expect to have a million moving objects on screen with full physics even if you can do that with the native (C++) library.
Flash vector graphics does not use the GPU and is rendered fully on the CPU. So if you need HUDs (heads up displays) with high-performance 3D vector rendering like what Scaleform provides for C++ apps, don't expect that to be easily possible in Flash Player, unless you're willing to roll your own 3D vector renderer that takes advantage of the GPU to composite vector shapes.