The Big angry bomb (BAB) is the most powerful bomb (per blast not DPS) and has an incredible knockback (enough to send the JK flying). Couple this with a massive blast radius and you have a nice bomb.
Unlike most blast bombs where you go and plant bombs nearby enemies this bomb is best used as area denial against monsters that use melee attacks.
This bomb creates massive knockback so playing the sword guy on a team with the BAB doesn't work well. Guns work well since they can hide in the blast zone (generally safe from monsters) and spam AT assisted shots. Bombing with a BAB bomber may work out good as you can lay down extra status types besides stun (see fire, poison) and possibly use your own blast bombs to "play volleyball" with the enemies.
For the BAB user I would suggest a CTR boost (with volcanic, mad bomber, or chaos cloak) UV or pet perk, till you reach LVL 10 on BAB and get that natural boost. After that you can change your pet perk to the damage boost.
The way I chain the BAB is by slowly moving the chain so as not to get out of the last bomb's blast radius, or by just chaining bombs in the middle of the field.
This bomb does best against moderate to slow melee enemies such as wolvers, mecha knights, knockers, and lumbers. It can fare well against cubes, lichens, thwackers, zombies and other mixed attackers.
Fast enemies like Greavers, or ranged enemies like devilites and tier 3 turrets (polyp, howlitzer, puppy) are more difficult to deal with.
The most noticeable downsides are slow charge, movement, and fuse time, the disruption it causes to average players (who have not experienced this rare bomb) and the comparatively low DPS (as this bomb is to be used defensively anyway DPS should not take precedence over party protection)
In my experience, the Big Angry Bomb should not be spammed. It's best use seems to be separating all of the monsters so that you can focus on priority targets, like healers. You could drop it in the middle of a room and then hop over to whoever you want to slash to death while the rest of the monsters are in disarray and/or stunned.
I don't think this is a good weapon on its own, nor is it good for spamming. (Because of the slow charge speed and movement speed.) Nitronome is a much better bomb for that. This bomb still has it's uses, though.