In the supplementary information of the study, there is a Table that breaks down the 22 food groups [1]. You can look at it yourself, but below are the consumptions for the "unhealthy" categories. Seems like Vegans eat more salty snacks and less sweet/fatty food.
| | Meat-Eaters | Vegetarians | Vegans |
|----------------------------------|---------------|---------------|--------------|
| Salty snacks and crackers (g/d) | 3.69 ± 0.06 | 5.28 ± 0.34 | 10.50 ± 0.48 |
| Sweet and fatty foods 6 (g/d) | 125.00 ± 0.52 | 122.00 ± 2.86 | 73.90 ± 4.00 |
| Sugary drinks (mL/d) | 23.40 ± 0.48 | 27.10 ± 2.65 | 22.40 ± 3.71 |
| Sugar-free drinks (x103 mL/d) | 1.08 ± 4.16 | 1.14 ± 22.70 | 1.05 ± 31.70 |