playing FLAC in foobar2000 with WASAPI at 841kbps to 1148kbps.

For playback, the file is decoded back into the original 1411.2 kbps data (assuming it was compressed from CD audio or other 2-channel 44.1 kHz 16-bit source).  You can verify that the bits are exactly the same as before.  The data that gets sent to the DAC is the same, through all the same mechanisms, so sound quality should be the same.

During playback?  Whatever it shows is up to the software player I guess.  It's the compressed bitrate—bits of encoded data / second—though exactly how it's calculating (averaging too?  over what interval?) and displaying the data, I don't know.

Convert it back to WAV or whatever else and compare the bits.  Actually, you can probably open up the FLAC and the original in some kind of audio editor and compare there.  Audacity is one free option.  Zoom in a lot and look at the data sample by sample.  Or invert the data and add it back to the original, and see that you get 0.  Or just play back all tracks (inverted plus original) and confirm you get no sound, and that you get sound whenever you listen to each separately.  Whatever is enough to convince yourself one way or another.

You can try the same thing with lossy compression and see that you don't get 0.  Note that you might need to be careful of everything aligning perfectly in time.  I think there was a program for this purpose... Audio DiffMaker?

Well, uncompressed 2-channel 44.1 kHz 16-bit music is 1411.2 kbps, so that's what it shows... The FLAC gets converted to the same PCM data for playback by anything that can play back FLACs.  That's the point of lossless data compression, isn't it?

If you're using fb2k, I recommend you download and install this plugin:

http://www.foobar2000.org/components/view/foo_abx

Select the FLAC and the WAV, right click -> Utilities -> ABX two tracks and do the listening over again.  It just asks you to identify whether the mystery track is either the FLAC or the WAV; it should be easy enough to understand when you see it.  Run something like 15 trials and tell us what happens.

I'm pretty sure the first file in the list is always A and the second is B.

Now which files did you compare?  One was converted directly from the other (FLAC -> WAV, or WAV -> FLAC)?  If yes, mind uploading a small sample of it (both versions, FLAC and WAV), or using some music that is public and free to distribute? (which you have passed 10/10 or similar)

edit: did you confirm the bits were the same in an audio editor or similar?  If you didn't, as a sanity check, maybe run ReplayGain and see if the adjustment values for both are the same.

The bitrate shown in the statusbar is pretty much meaningless for lossless files.

For example, a track with silence can be compressed very well, the resulting bitrate will be very low, if on the other hand the samples are wildly random the compression ratio will be lower and therefore the resulting bitrate higher.

But as mikeaj wrote, it will always decode to 1411 kbps for 44.1/16 audio.

For CD vs. FLAC, the FLAC is generated from ripping the CD?  You confirmed that the bits were the same (i.e. tracks from the same master and not a different release of the same music)?

Maybe check your playback settings in foobar and/or your sound card.  I had VLC player sounding better that Foobar, however after changing the File/Preferences/playback/output setting in Foobar they sounded the same.