My aesthetic sense seems to appreciate the second style better. Yet I realize the second course designer couldn't make a BRP 4 with those trees and vegetation even if they wanted to.
There are pros and cons, even just speaking esthetically. (I'm only going to talk aesthetically, not for scoring/fairness issues)
Regimented, straight lined, well defined courses - read very clear visually, and appeal to some. It shows effort and control over a wild landscape. (Ball golf courses as evidence of man's mastery over nature - came could be said of formal rose gardens) However, it also becomes obvious when something becomes out of place, or disrupted. And generally, nature detests straight lines, so it risks looks "artificial". Sometimes you get the feeling or sense that the hole design is "fighting the land".
Organic, flowing style (second pic): Originally likely cleared and formally mapped out, and likely maintained, yet truly "the Play Determines Form" over time. Hole is "going with the lay of the land" No straight lines, all curves, everywhere, with no hard edged boundaries. The flipside, is that to some, this looks careless and without intent. To some observers (outsiders that call the parks department) that might mean "oh my G...so much trampling!"
Again, I like the second pic if I had to chose, but I'd really really like a blend - Go with the organic hole design, but do go with top notch clean edged, "formal" done tee areas and linking paths. Shows you can be formal, but have chosen not to do so in the area of play. Howver, one or two regimented holes can work as being memorable - BRP is almost defined by that hole at this point, so its working in that regard.
OK, so that's just about esthetics and not player scoring effects, so I strayed from topic, right? Well, it could be translatable to see that organic style design leads to more organically generated recovery shots, and formal lines will create more uniform recovery effort challenges.