Not knowing if its worth it to dual wield and/or take Ambidextrous is a pretty major issue for gun bunny characters.
The advantage of wielding a weapon in each hand is that you can have a ready melee weapon in one hand and a ready firearm in the other, using whichever weapon that is best suited for the situation. If you are not ambidextrous then your attacks with your off hand cant earn edge and you also cannot spend edge on the attack (for example no called shot vitals, called shot disarm, anticipation, wrest, knockout blow, fire from cover, shank, tumble...)
Another advantage of wielding a weapon in each hand is that you can attack the same target twice (but you can also do this with a single weapon as long as it have full auto capabilities), once with each weapon, by splitting the pool. If you are not ambidextrous then you only use the AR of your preferred hand (even if it is have a lower AR at this distance than your off hand weapon) when judging if you gain an edge in the attack and Anticipation will also only apply to the preferred hand attack and not your off hand attack (without having the ambidextrous quality your off hand attack dice pool will still be split in two even if the attack action is combined with anticipation).
If you are wielding a weapon in each hand then you can also attack two different targets (but this is also something you can do by using a firearm that have burst fire capabilities), once with each weapon, by splitting the pool (and using the highest DR when calculating edge). Again, if you are not ambidextrous then you only use the AR of your preferred hand when judging if you gain an edge in the attack and Anticipation will also only apply to the preferred hand attack and not your off hand attack.
...and if you for some reason happen to wield a weapon in your off hand rather than your preferred hand then you can't gain edge on the attack and you also cannot spend edge on the attack, unless you are ambidextrous.
Having ambidextrous will not really make or break the game, but if you are often attacking with your off-hand then it might still be worth it. It only cost 4 karma, after all.