I'm worried that the Riff Raff will lack in bass frequencies and sound very bright.
The RR bridge is indeed quite bright but in a good way - no harshness, no ice-pick, just a lot of clear high harmonics, and the low end is not lacking, this pup works a bit like a good Tele bridge, it's kind of twangy but fattens in a really nice way with overdrive and the tone pot.
The RR neck is very clear and detailed but still warm, very dynamic / touch sensitive too, and really sings from pristine clean to bluesy crunch to heavy gain. I do like my two others BKP 'bucker necks (crawler and mule), but the RR is actually the one I use the most.
To make a long story short: RR are bright but neither thin nor shrill sounding.