Here is a highly biased thread addressing your situation with relatively good responses: http://forums.spiralknights.com/en/node/106308

Here is my response in that thread: http://forums.spiralknights.com/en/node/106308#comment-961939

Here is my response but copy-pasted so that we don't all have to open 20 new tabs:

"The lancer knights data suggests that every attack speed up would be about 3.7%. I have a hunch that it's probably 4% just like damage is, but it could just as easily not be, so I'll take the safe route and use 3.7%.

Your speed started at: 1.11 times faster than base speed at zero = 11% faster than base speed
And became: 1.22 times faster than base speed at zero = 22% faster than base speed

The actual difference between these is about 1.099 (as in, if you were to count the initial 11% as the new base, like you did in the video) which is about a 10% increase in attacking speed. This isn't very much, and I really wouldn't even expect anyone to flat out notice it... consider however, that the total buff of 22% is actually a pretty big increase. If you shot 100 bullets before, you're not shooting 122 bullets. This also effects the time it takes you to get your shield up while shooting- if it took you 1 second before, it now takes you about .82 seconds. Lastly, attack speed increase is NOT a straightforward damage increase. That means that you can further boost your DPS by 22%, but more than that as a compounded bonus- if you get 24% extra damage, attack speed increase will boost that to around 51% more DPS. All of that combined together is a pretty sweet and worthwhile get if you ask me.

As for just the very high, that would be a 14.8% increase. You can say that it's not enough, or that it's not fair, but it's still an advantage that you have out of nowhere. Not your armor, not your shield, not a sprite perk... just out of nowhere. Every time you use that weapon, that 14.8% increase will be there at no cost to yourself. What about this don't you like?"

....

Unless I've missed something within the last couple of months, this should be the newest thread (aside from this one) that discusses the value of attack speed increase. It DID happen prior to the gunner update in which the attack speed values of certain guns (namely pulsar lines) were changed, but it very probably still holds true.