Hm, well, I think they could do both. They could have a "free mode" where you can walk around the environments just to explore and see what Pokémon you find, and there your goal could just be to get a good shot and find every Pokémon. And then they could have a different mode where you ride on-rails through the same various environments and are scored based on your shots just like the original game. That would help keep it true to its roots but also expand upon it.
Of course, that sounds like too much work for the amount of effort they typically put into Pokémon spinoffs, which is a shame as I usually think they have good ideas, just not used fully.