I have tested Parallels -- running BIAB Windows 2012 on an IMAC with 6 GB RAM in the latest version of Parallels. I also own its main competitor, the latest version of Fusion, and for BIAB, Fusion is the only one that works for me. The main problem is, I'm getting some quiet-but-audible "clicks and pops" playing back BIAB in Parallels, which I haven't experienced in Fusion (and for testing purposes, I imported the same Windows machine into both). This has also been a problem for me in some (but not all) previous versions of Parallels. I actually slightly prefer the Parallels interface, and if BIAB wasn't my main reason for running Windows on a Mac, I'd choose Parallels. But BIAB ran really smoothly for me in Fusion, and I'm running the Audiophile version. I also found Parallels' tech support less than helpful -- though I haven't needed VM's tech support, and thus, can't compare.
Of course, your situation might be different, and it may be that BIAB and Parallels will run fine for you. It's obviously working for some folks.