I can't make a comparison with chickens but my turkeys love to graze all day if they can. They scratch bare earth or anything on it such as fallen leaves. Also, they like dust baths, preferring bonfire ashes if they can find them.
They are generally not destructive but have two bad habits:
1. Pooping anywhere they choose. This isn't too difficult to control to a fair degree if you move their water and feed to a place where poop isn't a problem. We tell ourselves that it's good for the grass.
2. They like young leaves and shoots, including new banana shoots. Depending on what you have on your land, you may want to protect your most precious plants. In our case, the new shoots develop quicker than the turkeys eat them.
All in all, we don't mind the things that they get up to. Our land is divided between a landscaped area and, well, just land. They have their favourite spots, mainly in the shade, and we work around that. They only thing that bugs us is their delight in sitting on a shaded upturned tree root and dislodging the orchids and ferns that my wife nurtures there. Apart from that, they have been little angels.
If you can, set aside some areas where they can graze and linger that aren't precious to you. Let them roam around your lawn and graze on the new growth - that keeps them occupied for hours.
Regarding chickens, our neighbours all keep them and my impression is that they make a real mess of the ground. That might indicate that turkeys are less destructive but it might also be because we exercise a little more care and control than do the neighbours.
