I don't think there is a significant difference.
Occasionally, there may be lower frequency music in the Center Channel, but not very often.
The lowest human voice (BASS) is about 60 Hz, so the CLR2002 should be just fine for dialogues. And when set as Small with a Crossover of 80Hz-100Hz, it is definitely just fine.
One case where the CLR2300 would have a clear advantage is when you are using something like a Denon SACD/DVD-A player. When set to SOURCE DIRECT, the sound goes directly from Digital (DSD) to Analog, bypassing PCM, bass/speaker management (setting every speaker to 20Hz-20kHz) and all tone/balance controls.
Another thing is, the CLR2002 has the 5.25" midrange, but the BP7006 has the 4.5" midrange (like the CLR2300). As a rule of thumb, most people recommend matching the driver sizes. It is probably not critical and most people probably can't tell the difference.
So for most applications, the CLR2002 is just fine.
...Until you get that Upgrade Bug.