Is there a side I should bet on to have more than 50% chance to win?
No, the asymmetries do not affect the fairness of the coin, if it is caught in the hand.
I draw this conclusion from: You Can Load a Die, But You Can't Bias a Coin, Andrew Gelman, Deborah Nolan. The American Statistician. November 1, 2002, 56(4): 308-311. doi:10.1198/000313002605. Full Paper
Dice can be loaded—that is, one can easily alter a die so that the probabilities of landing on the six sides are dramatically unequal. However, it is not possible to bias a coin flip—that is, one cannot, for example, weight a coin so that it is substantially more likely to land “heads” than “tails” when flipped and caught in the hand in the usual manner. Coin tosses can be biased only if the coin is allowed to bounce or be spun rather than simply flipped in the air.
We explain this phenomenon by summarizing a physical argument made in earlier literature.
As well as repeated experiments with students, they use a simple physical model to show that - as angular momentum is conserved - any coin will spend half of its time heads-up and half tails-up. If the coin is spun or allowed to bounce, this model falls apart.
Note: Fake double-headed coins exist. [Ref] Also, magicians exist: Sleight of hand can be used to make the original coin vanish or for the result to be read before the coin is revealed. [Sorry, only anecdotal evidence: I can do that. I can't quite manage to force a result based on the call in the air - I can't think fast enough to make it look fluid - but I see it as feasible with practice.]