"prefer either" is correct English usage.
You can use it when you want to express that you have two choices and that you are leaning more towards one option than the other. For example: "I prefer either the blue shirt or the yellow shirt."
Personally, I prefer either of those to this feel, but that's a personal preference.
It is no disgrace for any country to prefer either one over the other.
But Zardari, who traffics heavily in metaphors of combat, seems to prefer either guile or trials of strength.
But investors lacking analytic self-confidence may prefer either open- or closed-end mutual funds or E.T.F.'s.
They prefer either traditional Chinese ink paintings or works by current art-world stars such as Antony Gormley, Damien Hirst, and Olafur Eliasson.
But my answer is always the same when I'm asked what outcome I prefer: either result will be the correct one.
She prefers either buying a carcass from an honest farmer or using tough untreated stew meats.
The first prefers either very long metres or very short, employs a simple, non-Persianized language, and restricts himself to affairs of the heart.
Roughly half of those people have been undecided since last year, but the other half have become undecided over the course of 2012 after initially preferring either Obama or Romney.
But three-quarters favor quotas under the condition that the qualifications of candidates are taken into account without automatically preferring either sex.
All three oppose President Obama's health care program, seeing it as a giveaway to insurance companies and preferring either a single-payer government plan or a socialized system like that of Britain, where doctors work for the government.
