I'm asking about the total change in entropy from the original solar photons to the final building. Far more goes into that than rearranging bulk objects in the final step. Trees growing to form the wood, etc.
All of these processes involve entropy generation. Trees etc. are basically a collection of mini-engines that process low entropy fuel (photons, food) into generating useful energy, fixing themselves, growing, and emit waste products like any engine.
All of the above-mentioned jobs living things do can be described like this: the living thing is trying to lower the entropy of some subsystem (basically itself plus the building blocks from which it grows), at the cost of increasing the entropy of everything else.
Of course all of these processes are not even close to 100% efficient, so all of them result in a net entropy increase. At an even more basic level we can just say that all of these processes are off-equilibrium, irreversible processes, which again means a net entropy increase.
OK, so which results in a greater net entropy increase, a skyscraper or a small building? You can just view building a skyscraper as essentially first making a small building, and then adding many more stories on top of it.
More irreversible processes (powering our machinery, using our muscles etc.) to convert natural stuff into stuff we want means more entropy generation.
We should be careful here about what we are actually comparing though. If the comparison was, say, between:
(A) using a bunch of low entropy photons from the sun to generate energy and everything else we need to build the skyscraper, and
(B) letting all of those same photons to just fall on the ground and heat it up, instead of being caught by plants or something else that wouldn't waste them and would use them to lower the entropy of some subsystem
then the answer would obviously switch, constructing the skyscraper would result in a smaller entropy increase!
We can stop the answer here, but let me just make one more quick comment. As others said, rearranging blocks to make a building out of it contributes very very little to a decrease in entropy (if at all, depending on exactly how you view entropy). I think you were wondering more about making the blocks as opposed to rearranging them, but if a block has a lower entropy than the building materials that went into it, then that would just be another example of one of those subsystems whose entropy was lowered by some sort of engine with a less than 100% efficiency at the cost of increasing the entropy of everything else by a bigger amount.