In both instances Kayneth's opinion is basically "seems alright, no problems here." He's a little more fond of Archer and a little less fond of Ryuunosuke, because well a) he loves himself and Archer is basically a palletswap, even if he probably wouldn't consciously acknowledge that, and b) Ryuunosuke has the kind of personality that he finds mildly annoying but can put up with.

...if he finds out Ryuunosuke was Caster's master in the Holy Grail War, though, he's going to be super buttfurious at him forever, haha.