A number of months ago now, we switch from (Telecoms old plans) the 20gb per month plan to the 40gb per month plan (+ the 20gb extra they added on). I play online games, and my latency to Syndeys Call of Duty 4 servers went from 90-100 down to 60. I was amazed at this.
We started using more and more internet and we switched from the 40gb plan to (the new plan) 150gb. The latency went back up from 60 to 100. We are now on the 500gb plan, and the latency is still the same
I have tried using different modems/routers (I am currently using a NetGear N300) but to no avail.
Unfortunately I do not have a speedtest image from when I had the faster internet (I noticed the speeds were a tad faster then) but here is one I have just ran:
To Sydney:

To Wellington (I live in Masterton):

To Auckland:

And Pingtest to Auckland:

If you need any mroe info, please ask and I will try my best to supply it to you