An informative site by Mr. Stephen A. Camp related to the BHP may be found at
www.hipowersandhandguns.com
One of his articles therein on comparing a CZ (albeit a CZ75, not the P-01) to the HP
http://www.hipowersandhandguns.com/CZ-75 or BHP.htm
As others have said, both are fine 9mm's. One design being a bit more recent, mag disconnect and trigger action being the key to my way of thinking... (SA v. DA/SA and carry method; but since you're from the Chicago area I gather open carry or CCW is not an issue). Both are relatively good enough from the box for plinking and regular shooting fun. Serious shooting might require some break-in or trigger work to smooth things out, maybe removal of the mag disconnect in the HP, which means more money spent on some smithing (unless you know your way around BHP's).
If $ is an issue, the CZ product is probably a better bang for the buck NIB, but I just had to have both (CZ75 tho'). If pretty is an issue (I likes me a handsome handgun) then the polished blue BHP walks all over the baked on finish my CZ wears (tho' the new stainless 75 is lookin' pretty good... kinda).
Both are more accurate than my eyes allow me to shoot (excuses excuses).
Both have interesting histories behind them.
Both are worth owning... so plan on eventually having one each.
The CZ has a bigger family if you find collection fun. But, the same can be said for gathering foreign made HP's (Canadian, Belgian, Clones from here and there, WWII era, etc)