In my experience, First Class/WBC/Elite tags only makes a difference when traveling internationally. While it's still not consistent, when I travel to Japan, it's usually amongst the first one out.

When I travel from Japan to the US, it's amongst the first one out at the us custom inspection area. It's however not the first one out at the final destination though.

I don't know about transatlantic travel since I hardly ever check bags for tranatlantic travel.

Others who frequent this web site, however, had differet experience.