Either version would be interesting. The nice thing about the Walker skill is that it allows (1) normal walkers to turn round; (2) lemmings performing a continuous skill to stop (or builders to stop early); (3) blockers to stop blocking without exploding themselves -- and in any given level, you generally don't know in advance which function it will serve (though the absence of blockers removes one possibility!) so there are a variety of approaches you can try out. This can lead to backroutes, but if the designer has been careful, it can make the solution process more interesting.
The choice between the two varieties of Walker doesn't affect this much. Indeed, for bashers, miners and diggers, the two will often be equivalent, as the terrain would turn them around anyway. For builders, Lix/NL behaviour means the builder-walker will immediately step off his bridge -- depending on the situation, this might be exactly what the player wants or exactly what they don't want.
Personally, I'd prefer you to go with Lix/NL behaviour just on account of consistency: that would make it easy to design levels for your game that could easily be ported to Lix and NL (which I would love to do). But no big deal if you prefer to do it the other way. Most levels will still be easy to port, or could be made to work with minimal changes.