Both images actually have some good compositional qualities to them, but your “beauty” photograph is undoubtedly the stronger photograph. What you’ve chosen to do to enhance this image is focus your attention in on just 1 of the elements of the photograph removing all references to tables, walls, floors, pots etc. The beauty photo is enhanced through simplicity and focus limiting the objects within the frame to just the flowers and a slightly textured backdrop with a neutral color.
The simple textured background helps isolate your main object, while giving an interesting secondary object to look at. There are small details on the surface you’ve placed your flowers that are inviting to the eye.
Overall, your image is very well composed. I have two recommendations that I would like to you to consider though. First, you’ve amputated (cut off) a very small portion of the top of your flower petal with the top frame of the photograph. I find this mildly distracting because it looks accidental. It would have been optimal to include the entire flower petal without snipping it off at the last moment with the top wall of the photograph.
Secondly, the lighting is a little flat. It’s not wrong what you’ve done, but I think your subject (the flowers) lend themselves well to more texture friendly lighting. Getting some directional side lighting in (even using a table lamp or a flashlight) and playing with direction and intensity would have helped draw the texture in this photograph out.