ING does increase quality by a bit, since apparently quality increases are also influenced by level difference. How much it actually increases is a different story, and whether or not does it justify the 32 CP cost.
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Some numbers for BB, 407 control, first number is IQ count, some numbers may be off by 1 due to calculations after Good condition/Great Strides:
Code:3* base INN INGII INN+INGII
08 717 869 813 985
09 842 1008 955 1143
10 978 1159 1108 1314
11 1125 1321 1275 1497
4* base INN INGII INN+INGII
08 866 763 924
09 840 1005
10 975 1156 1040
11 1122
I usually go for innovation because it is cheaper. Honestly, what is even better than ING2 is to stretch your craft out longer and get more touches. One more successful touch will net you more benefit than either of those skills will. I used to try to save enough cp out to do ing2 and inn. Now I make sure I have enough for gs, bb, and sh, and will take chances purchasing durability for more touches. If I get some good conditions and have enough for inn and ing2, great. If not, I'm better off finishing at 10 stacks without them than at 8 stacks with them.