Depending on the method that the Eidolon is summoned (if it matters) how does control summoned creature affect it?
Yes, Control Summoned Creature can control an Eidolon.
Summon Eidolon states that:
Treat this as if you had summoned your eidolon normally
And both versions of the Summoner, chained and unchained, state in the description of the Eidolon class feature:
Eidolons are treated as summoned creatures
... with a limited number of exceptions to the normal rules for summoned creatures, none of which would prevent being affected by this spell.
Since the Eidolon is a summoned creature, and no other special quality clarifies that it should not be affected by this spell, it is therefore vulnerable, and can be controlled in the manner specified by the spell if it fails its will save.
From the eidolon class feature:
A summoner begins play with the ability to summon [...] an eidolon. [...] the summoner, who [...] summons an aspect of the same creature. [...] Eidolons are treated as summoned creatures
From summon eidolon
School conjuration (summoning);
In both cases the effect is clearly a summoning effect, the eidolon is clearly a summoned creature, and therefore the eidolon is subject to control summoned creature.
Control summoned creature says "by disrupting the bond between it and the caster who summoned it."
Many summoner descriptions refer to the bond between the summoner and the Eidolon, so my intuition is that this bond is sever-able.
Considering the level of the spell, as well, my intuition is that that is perfectly acceptable. The original summoner might still be able to banish it however (with one standard action).
Also, regarding the original question, I would say that it doesn't matter if it was summoned by ritual or spell in this instance, for the same reason.