Re: Choice of drink can overwhelm cigar's flavor...
 

I tend to prefer alcohol with my cigars. At least after work.
Mostly on the rocks. Or neat. But I'm not usually a neat guy.
Some are better with light rum or martinis, such as lighter to medium strength. Others dark rum, especially medium maduros.
Then there are those that pair with scotch (lighter body), and the rest, being of a more full body, which pair with bourbon.
Except the ones that work well with tequila (Honduran for the most part).

If beer overpowers your cigar, I'd recommend a good coffee.