The numbers I've used are based on the current AP regen numbers on the wiki. In particular I will be comparing two situations, Relative DPS while standing still with double tap, and relative DPS assuming the 12.5 regen never kicks in. These situations are not always realistic, but will allow to establish a general pattern of how each perk scales with AP cost and AP regen. I have not taken into account critical hits, or the time a weapon spends in it's animation before it is allowed to refire.
The primary metric I will be using is relative DPS. Since each perk essentially multiplies the DPS of your weapon, it does not matter what the weapons damage is as the damage will always be the same. For example, a relative DPS of 1.15 would mean that with the perk you would be dealing 15% more DPS than without it. I am calculating relative DPS in the following way:
DPS (with perk) / DPS (without any perks)
Where DPS is calculated with:
AP regen / AP cost
The base DPS value shows you how much of your weapons damage you will deal on average, per second. The Relative DPS values show what this number is multiplied by when bRoF or AB is taken.
Similar to my last post my conclusions are based on a spreadsheet I've constructed which may contain errors. This spreadsheet has multiple pages. The first deals with AP regen including the 12.5s for doing nothing or having double tap. The second uses only the AP+ value. The third shows what happens when Fast shot is introduced Because recurring numbers make the spreadsheet less readable I have changed the formatting to use rounding, but have created a second spreadsheet with non-rounded values. This will slightly influence some of the values seen, but in most cases shouldn't fundamentally change what anything means. The spreadsheet itself is very large because I wanted to show differences between a wide range of values for AP cost to shoot, but as it turns out it does not change the statistics in an important way. These areas remain as proof of that.
Rounded:
https://docs.google.com/spreadsheets/d/1NlmXBVVwk-Aw4xSvMbZkFCdioxY9xexTsFpfx3CkYUo/edit?usp=sharingNon-rounded:
https://docs.google.com/spreadsheets/d/1mXwRZtzHim3yzreZ0q_cf90FKI9s05RRpevZYohp11k/edit?usp=sharingHow does the AP cost of a weapon influence these perks?
How important is your existing AP regen and Agility before the perk is added?
What if I have Fast shot?
So when will one give me more DPS than the other?
Closing notes
Answers to questions
Taking Action Boy if you already have Bonus Rate of Fire, and possibly Fast Shot
Spoiler for Hiden:
Perhaps I should have been more Clear on this, since most of my post was comparing the two against each other.
If you have Fast Shot, it makes Bonus Rate of Fire a bit more effective to take. In terms of how much AB multiplies your DPS having fast shot doesn't change anything, but that doesn't directly make AB worse when you have Fast Shot, just less preferable to Bonus Rate of Fire.
At 5 Agility and full AP Regeneration AB will grant 5% more DPS regardless of whether or not you have Fast Shot, bRoF, or both. But, since having Fast Shot increases your DPS in the first place that 5% will be a greater number. For example, if you have 100 base DPS and no fast shot, AB will grant 5 more DPS in that scenario. If you take Fast Shot first, then your DPS would be 111, and therefore AB would add 111 *1.05 = 116.55DPS. An increase of 5.55 which is actually greater than before but still only 5%. In the same case bRoF would increase 111 by about 13% (Compared to it's 11% without fast shot) which means that not only will it scale with having a higher DPS, but the multiplier will become greater with Fast Shot already taken.
If your build doesn't have too high an Agility already, or you just want to maximize DPS, then AB is still worth considering if there aren't any better perk options left for that slot.