The thing about walking (like almost anything else in music) is that what is appropriate entirely depends on context.This is the first time I've heard that about the 2. R-5-8-5 will play a lot of bass and they are all chord tones.
For rockabilly or bluegrass, the R-5-8-5 would work perfectly for most of your bassline, whereas for post-bebop jazz it would sound corny before you've played 2 bars.
Conversely, playing a Gary Peacock walking bassline on a bluegrass tune would get you fired before the end of the first chorus.
You have to understand what best serves the music in your case. Listening to what the great players in your genre play will help you sorting this out.