As far as nail damage is concerned, flexi tip nails are less likely to damage your natural nails. Unless you roughly rip it off.
Mostly, it is common to experience dryness and brittleness after removing the press on nails. This is because we dip our nails in acetone for a more extended period and acetone dries our nails and skin.
When it comes to acrylic nails, they are pretty damaging, especially when reasonable care is not taken. So, you need to visit your nail technician after every two to three weeks for nail filling.
Otherwise, the gap between your natural nail and acrylic nail may suffer from severe fungal infection due to moisture. In addition, over-filing your nail bed can weaken your nails, causing pain and infection.
In short, flexi tips are safer than acrylics.