Your LHS is describing the right problem to you-- the tradeoff between stability and maneuverability is as old as airplanes and very real. WRT the Axe vs Blade question, I think they're probably telling you right as well.
I'd be very interested if someone else has bought both and could post thoughts on the matter. I have the Blade CPP, so figured I'd weigh in a little in the meantime. You might not expect it since I have the Blade, but if the choice is between the two of them as a starter CP, then I'd recommend trying the Axe first-- but with that caveat, that I haven't gotten one for comparison myself. The main difference I see is that the Axe is a much stronger aircraft, which likely extracts a penalty in responsiveness. This is not a bad thing by itself, only if it conflicts with what you want.
The BCPP has a lot lighter construction than the Axe (parts of the Axe are positively beefy by comparison), and its mass is concentrated around the roll axis, so I expect it is significantly more responsive to the controls than the Axe as a result. I know from my own experience and reading various threads that the BCPP is challenging starting out as a result. You can get spare parts for it everywhere, and they're substantially cheaper than the Axe, but that suggests something about how well they sell, doesn't it?

When you hit something with the BCPP you almost always break or bend something. The BCPP has a lot of room to grow, though; when you do have to replace something you find you also have a huge aftermarket supply of upgrades and mod parts to choose from in addition to the OEM bits.
Personally? I don't crash it any more except when I'm trying something new, and it's a fun plane to fly when you set it up right. But there's no question that it's the hardest helicopter to fly in my little stable, by a wide margin.
Above are some thoughts, not a conclusion, really-- it really depends on your priorities and skill level. If you are looking for your first heli, by the way, I'd actually say; "neither." Take a look at the Honeybee FP instead. It's a much gentler introduction to micros than either one of these, and it's darn near bulletproof.