I have both of these bags, but in different prints. The DZP is super light and slim on the body. I have an iPhone mini and it can fit with case in the slip pocket, which I love! You do have to be a bit careful with how you pack this bag as it can become wonky looking easily. Great bag for just the essentials.
The Gucci bag can definitely fit more, and fit it easily. It’s also more structured, and sticks out bulkier from the body. I love mine, but usually wear it on the shoulder, bc I don’t like where it hits me crossbody. This bag in the prints you chose would be more carefree in the rain, etc. since it’s treated leather and coated canvas, versus the vachetta on the DZP.
overall, they’re both really nice bags, and I think it depends on if you’re looking for something slim that just fits the essentials, or something a bit bigger that fits more than the essentials.