Do high-wing aircraft represent more difficult engineering challenges than low-wing aircraft?
Actually, in aircraft construction tension is preferable to compression: aeroplanes are thin walled structures, and compression forces introduce buckling.

In a low wing aircraft, the fuselage is pressing downwards on the top half of the wing, the bit that is under compression. In fact, quite complicated frame structure members are required for the fuselage/wing intersection for low wing aircraft: they need wing dihedral, so the wing looks pre-buckled at the spot of largest bending moment.



So although high vs low wing does have some differences in structural implementation, those are not the deciding factors in the layout. The design considerations for operational use are what drives the choice high-low-mid wing. Picture below from Torenbeek, depicting the Galaxy C-5.




High wing designs are usually applied for aircraft that need quick loading/unloading, and/or operate from airports with limited ground equipment.


Wing out of the way: good for loading/unloading, and for long extended flaps on STOL aircraft.
Floor close to the ground: easy cargo handling, good access for passengers, no need for airstrips.
More room for propellers.
Lowest induced drag at high lift.
Self stabilising roll behaviour.

Mid wing has the lowest drag of the three layouts at high speed, but poses a particular problem in running the wing through the fuselage. The wing must be a complete structure, because it has the highest bending loads in the wing centre and we don't want any holes there, best to make the hole in the fuselage to lead the wing through. But this bit of the fuselage cannot be used for passengers or cargo.
Low wing is usually applied in passenger aircraft because:


The undercarriage can be easily retracted.
The wing forms an impact structure that absorbs energy in case of a crash. Although the fuel tanks are in the wing...
The wing is fully underneath the floor and does not impede on the thoroughfare in the fuselage.
Optimal use of ground effect during take-off and landing.



In the 1950s, for the F27 the decision was taken to implement a high-wing design for its intended successor to the DC3: market analysis showed a significant market share outside Europe and the USA, at airports without the latest facilities. From wikipedia:




  while a high-mounted wing had been selected as it produced a higher lift coefficient than a lower counterpart, it also enabled easier ground loading due to a lower floor level and provided unfettered external views to passengers without any weight increase. 


And who wouldn't want unfettered external views?