Are the building blocks of complex circuits built of gates or transistors?
Absolutely. If you're doing high performance, full custom chip design, anything to get an edge will be done, including transistor level design of critical blocks. However, even at a standard cell library level, things like adders are implemented using more complex blocks than simple AND and OR gates. A full adder can be built out of a more specialized collection of transistors than what would directly correspond to the equivalent logic gates. A standard cell library will include several variations of full and half adder cells alongside the more basic AND, OR, NOT, XOR, etc. gates, as well as some common combinations such as and-or-invert (AOI) and similar that are relatively common and can be built more efficiently at a transistor level. Same goes for latches and flip flops. You won't use a pair of cross connected gates for a latch, you would use a specially designed latch cell.