My style is somewhere in between. It's still somewhat scattered to create a natural feel, but far from the degree of the second map. I usually do make consolidated areas of grass, but like Sparta, I then remove individual tiles from the inside, and I also add a few on the border to stop it from being a perfect rectangle.
Something that's worth noting is that while your Route doesn't need to have any mandatory grass, a path with grass is often used as an alternative to something else (a one-way grassless path with ledges, a way around the grass that makes you fight a Trainer, a path that's blocked with an HM or puzzle so you can skip the grass if you have that, et cetera). Even if you have a few mandatory patches of grass, a lot of it will be an alternative like this - so you need to map accordingly, because if you're given the choice between a path with a Trainer or a path that has "some grass but it's scattered so you don't have to touch the grass anyway," it's a lot less interesting or compelling as a player than a path with a Trainer or a path where you actually need to go through grass. It's also used to keep items off the beaten path and make players question whether they should go get that item or not, but again, if you don't actually need to go through a few consecutive tiles of grass to reach the item, it's not a very effective way of doing that.
Generally, the first screenshot is a lot more conducive to appropriate and interesting use of grass, so I would go with that. There are ways to make it slightly more visually interesting (remove grass in the middle and liven up the border by making it uneven and erratic), and usually the empty grass patches in the middle are good places to put hidden items where players will know to look, so that serves another purpose anyway; still, at its core, that's just the first screenshot with minor aesthetic changes!
I also don't like individual/lone tiles of grass that are neither close to a full patch nor serving to block anything, which the second screenshot has all over the place, but that's just personal preference because it looks out-of-place - I see a difference between having some stray grass right around a patch to make it look better versus having stray grass randomly placed for aesthetic, because it doesn't really make your map look pretty or more natural - and why would a Pokémon be hiding in tall grass if there's only one tiny patch of grass that can't hide anything?
Somewhat related, an interesting thing to consider is how grass arrangement is affected by the game mechanics specific to a Generation. You guys know how Sinnoh is famous for such big grassy patches with such low encounter rates that even the grassy routes might as well be more of the famous Sinnohan caves? And, in particular, those big grassy patches are often a minimum of 9x9 and square with minimal decoration? Well, that might seem at a glance like bad game design, but only until you realize that those patches were specifically designed to be used with the Poké Radar - they're simultaneously a small challenge for players and a convenient mechanic for postgame that just give you the most fascinating look into how Game Freak maps- oh, nobody cares? Sorry, haha.