The 'Blues Harp' is just a name for a wood combed diatonic that is made by the Hohner Company. It is no better for playing blues than any other harmonica that has 'Blues' in it's name. This is just smart marketing by the world's largest harmonica company. If anything, because it is made of wood, it can be much more difficult to play whether you are trying to play blues or any other style of music. They are really two different instruments .
Most good players specialize in one or the other.
It is rare to find players that really excel on both, but they are out there. It sure is. If bending was a prerequisite for playing the blues, then there would be no such thing as blues piano. Since a chromatic harmonica has all the notes available, not unlike a piano, you might be better off with the chromatic for what you want to do. Quality wise it tends to be just the opposite.