I've fired the BHP and owned a beagle 9mm. Of the two, the Baby Eagle is superior in almost every way. It's better ergonomically, it has a double action trigger, the trigger is smoother, the gun is more accurate due to the rifling (can't / shouldn't shoot cast reloads), the sights are better. It also costs about $250-$300 less.
I was facing this exact same decision about a year ago. I loved the beagle, but couldn't stand only being able to shoot jacketed bullets. The slide safety annoyed me to no end, and I had to use an Uncle Mike's fabric holster, because the only other thing that would work was a cz75 product, and it was $125. I looked at the BHP, which is why I said that I fired one, and had a friend take me out. I put about 500 rounds down the pipe over 2 months, while testing other pistols. In the end I picked up a CZ75 SP-01 Tactical, because it was a lot like the baby eagle.
The downside to the Baby Eagle:
The finish sucks, stuff comes 'loose' on it a lot. Most notably the rear sights and the grips. The safety is on the slide, which is just absolute crap. You can get one that's not on the slide I believe though.
Here are the upsides to the BHP:
They've been around forever so everyone will tell you they're awesome.
If I were you I'd expand my decision from BHP vs Beagle to:
CZ, BHP, or IWI
Ultimately I think you'll end up with a CZ, as the price of an SP-01 is still less than the BHP and the gun is better in every single aspect. it even has the same look/feel/handling and weight.