Luck seems to have little to do with the Stone Summons.
It seems to have a direct effect on the drops you get upon defeating enemies (Bad luck = All Blue souls, Great Blessing = All Silver Summon Stones, Betweens = a bit of both), and perhaps what is made out of Destiny Summons.
I like how each level of luck has it's own world map theme.
-------
Am I the only one that feels like Number of monsters is more meaningful than quality of monster? My lvl 20 Undine hits almost as hard as many of the SR summons I call as partners (sometimes harder?), and it's much easier to raise her with bonus stats due to being able to fuse her with duplicates.
Compare that to a SR, which you might only get a 2nd of once in a blue moon, causing him to level up slower. And it's much easier to get a clone of a UC or R for breaking level caps, than to get another for a SR.
I mean, they have great skills and abilities, but having 2 or 3 monsters of 2.0 in a fight rather than 1 monster of 5.0 doesn't seem like such a difference to where I feel like it makes the game more "pay to win".