The smart money says atoms can't exist in 4D. However if we go with that then we have an empty Universe. No fun in that. So let's assume that atoms or some equivalent exist. (I'd put my money on knotted electromagnetic vortices but nothing much is known about them. Better to pretend our familiar atoms exist. )

The one dimensional quantity of distance is the same no matter how many dimensions you may have. A diameter is a distance. So let's assume our 4D atoms have the same diameter as 3D ones. We are already in fantasy land so we may as well have simplicity. The same mass too. Then for the sake of definiteness let's say that 4D things have the same number of atoms as the corresponding 3D things. Surface area is measured in the number of atoms exposed on that surface. Now we can compare 3D and 4D objects in a systematic way.

An extreme example is a string of single atoms. Its length and surface area is the same in 3D and 4D. At the other extreme is a sphere, but let's make it easy and go with a cube. A 4D cube has more surface area than the corresponding 3D one. Consider a cube with a trillion atoms. The 3D cube has ten thousand atoms per edge, the 4D cube has only a thousand. The 3D cube has 6*10^8 atoms on its surface, the 4D cube has 8*10^9, that is 13 1/3 more surface area. Go to a trillion trillion atoms and the ratio becomes 130 1/3. The ratio increases with the twelfth root of the number of atoms. By the time one gets to a human body the increase in surface area and decrease in proportions is about a thousand, while with the Earth it is ten thousand.

The huge increase in surface area means that objects have much more drag. Jump off of a cliff and with a thousand times more drag your terminal velocity is something like 10 mph. And with a thousand times more lift one might have difficulty approaching that terminal velocity. Not only that, muscles though tiny are a thousand times stronger. This is because the strength of a muscle depends on its cross section. A cross section is an virtual area, so it is a thousand times greater. So a muscle though only 500 micrometers long would be a thousand times stronger than ours. With all that lift and strength one can imagine flying elephants. Dumbo would be only a centimeter tall but equally massive as a 3D elephant. Not only that, bones would be a thousand times stronger as would be the connection between bone and muscle. The wings can be fairly small as with insects, not dominating as in birds. Indeed the bird design would have too much surface area, too much drag and difficulty with control in winds. Dumbo rules. Birds lose.

The same sort of thing plays out in our world. The scarab can lift over a thousand times its own weight for these very same reason. It's surface to volume ratio is about thousand times greater than ours so its muscles have a proportionally greater cross section. A scarab can achieve equivalent to a human lifting a hundred tons in a single go.

I thought there would be an increase in friction. Could 4D people climb up blank walls? I'm not sure yet but I think no. Insects owe such abilities to specially adapted feet. Friction is supposed to be independent of surface area. How about walking on water, taking advantage of surface tension? Dunno, but today I'm guessing not. Insects do it with special hydrophobic feet.