What you have to worry about is "Mommy Guilt" If she starts thinking she is being rejected it's going to be hell in your house.

Let her be Mommy every now and then, she will enjoy it and you get a break.

and don't tell her how to fix the problem either, even though moms have been doing this to dads since forever,

I'm Not a Slacker

If you have a high tolerance for crying, you should allow him to cry. I think it's most important to teach him to cry it out at night (after the age of 6 months)- others will disagree maybe.

I don't think that the problem here is actual favoritism. Perhaps the true problem is that he is receiving too much attention from you for things he whines about. I say ignore the pouting for a while, and focus on the times when he deserves attention (like when he's in pain). My rule about favoritism is that the "favored" parent should protect the "unfavored" parent from rude and unkind actions (such as hurtful language- "I hate you" and hitting). My opinion is that such behaviors are unacceptable at any time, but especially when directed toward another family member, and should be met with a fair punishment.
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http://www.altparenting.com

The best way to deal with this situation, is a well relaxed conversation with your other half.

I did have the same situation with my now 2y6m old son, but now he is OK and we share the good and the bad (tantrum) times.
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Itux

Probably what has happened is your child has learned you will pick them up whenever they whine, whereas your wife is not as coddling. In our house, my wife is more coddling, so the girls always go to her when she is home. I have one girl about the same age as your child.

First, try to be patient and give your wife a chance to console the child, instead of jumping into action. I think you taking the child from your wife to console him could also send the message to your wife, that you don't think she is capable. Try having your wife take the child into a different room, that you are not in to console him. Out of sight, out of mind works good with kids this age.

You didn't say whether your wife has a problem with how things are or not. If your not sure, then talk to her about it. If it isn't an issue, then all you have to work on is breaking the cycle of automatically consoling your child.

"Natural Mothering" is a school of thought that says you should console them, whenever they cry or whine. I don't really agree with this method, but who knows what is really right or wrong when it comes to this topic? That is something you have to decide.