HQ and NQ stat gap needs to close (Both should allow max stats with materia):

[Caimie_Tsukino]

In order to verify what Ksenia said is true or not, I went on to do the following experiment.
First, I tried to obtain a HQ lvl 52 mainhand tool and a NQ lvl 55 mainhand tool. However, the stats were not what Ksenia had described. As you can see from the picture below, the NQ lvl 55 tool is actually 3 Control fewer than the HQ lvl 52 mainhand tool.

In order to proceed with the experiment, I have chosen the NQ lvl 57 mainhand tool. It does have 5 more control and 10 more craftsmanship than the HQ lvl 52 tool, so I melded 5 more control to the lvl 52 tool using materia. Now the two tools have identical control levels, and can be used for comparison on quality gain per touch.

Following Ksenia's description, I have chosen a level 55 recipe - Star Sapphire


If what Ksenia said is true. Then the NQ lvl 57 hammer will give much better quality per touch since it's 2 levels above the recipe. Where as the HQ lvl 52 hammer will give much less quality per touch since it's 3 levels below the recipe.

The results are as follows:

Using HQ lvl 52 tool with melds
Total Craftsmanship = 668
Total Control = 659

Basic Touch #1 = 269
Basic Touch #2 = 320
Basic Touch #3 = 372
Basic Touch #4 = 425

CS II progress = 247


Using NQ lvl 57 tool
Craftsmanship = 678
Control = 659

Basic Touch #1 = 269
Basic Touch #2 = 320
Basic Touch #3 = 372
Basic Touch #4 = 425

CS II progress = 251

Conclusion:
Both hammers give IDENTICAL amounts of quality per touch.
I am unable to verify what Ksenia had described.
I would consider it myth BUSTED.
There is one caveat in this experiment, and that is me being level 60 while Ksenia is level 56.
However, considering the fact that we're talking about i170 on this thread here, we should safely assume everybody to be level 60 (or they won't be able to wear the i170 at all anyway).