If I could fly anyplace direct from LAX on NW (I have no business or personal interests in Detroit, Memphis or the Twin Cities), I'd be more likely to check bags. Since everywhere I go involves at least one and often two connections, thus one or two extra opportunities for my things to go missing, I stick to the rollaboard + biggish computer bag scenario. Both my pieces are a tiny bit bigger than regulation allows, but I've never had a problem getting them onboard on NW.

Part of the reason I prefer to carry both bags when I connect is that the computer bag is always stuffed with heavy things like books (as well as the computer and its accessories), so I need the rollaboard to support the computer bag--I hurt myself if I try to carry it over my shoulder!

I often fly direct LAX-AMS on KL, but they used to lose my luggage more often than not on the nonstop flight (!) so even then I stick to carry on.