What difference in ball reaction for asymmetric or symmetric?.

As bill implies, there is no set ball reaction for either one.

Asymmetrics seem to have the potential for any one ball to have more ball reactions "dialed" into their drilling, due to the additional factor of the MB strength and its placement, in conjunction with the pin. Once drilled, the ball reaction is basically set because the drilling takes into account almost every parameter of the bowler's delivery/release. Using a different release with that ball will not usually get you a different ball reaction.

Symmetrics have a lower variety of ball reactions (but still, potentially, many), again depending on the ability of the bowler. The additions of weight holes in the proper places have the potential to change the ball reaction, as they do with asymmetrics. Also using a different release with the drilled ball will, more easily than asymmetrics, get you a different ball reaction, again depending on the bowler's capabilities.

Making the best use of asymmetrics often (but not always) requires a more consistent release on the part of the bowler, than a symmetric does.

THE MAIN DIFFERENCE BETWEEN SYMMETRIC AND ASYMMETRIC BALLS

A symmetric ball will give the greatest amount of track flare (oil line sparation per ball revolution) when drilled with the pin 3 3/8th" from the PAP, and flare will decrease with shorter or longer Pin to PAP distances.  An asymmetric Ball will give the greatest amount of track flare with a Pin to PAP distance of 3 3/8th" AND LONGER, flare will decrease with shorter Pin to PAP distance, due to the added RG differential of the mass bias.

REACTION DIFFERENCES

The only reaction differences between symmetrics and assymetrics occur with Pin to PAP distances of greater than 3 3/8th", the longer the length, the greater the difference.  A symmetric ball with a 6 inch pin to PAP will have little or no track flare and it's response to friction (hook) will be later in the pattern when the oil on the ball gets 'erased' by the dry backend.  Hook will be delayed farther down the lane on successive shots on a fresh pattern as more and more oil gets carried down the lane.  An asymmetric ball with a 6 inch pin to PAP WILL NOT carry oil down the lane on successive shots (other than the small bowtie oil spots) and will respond to friction immmediately when it exits the oil pattern on each shot.
This difference allows someone to drill a ball with a 6" pin so it will be thrown with a lower rev rate (a 6" pin is the high RG core position, which makes it harder for the hand to spin it) for more 'control' but still have the most aggressive backend reaction, without shot changing carrydown.