Would this circuit work like an SR latch? Why is it better to use two NOR gates?
Nobody ever implements individual SR latches in circuit design except within an integrated circuit.

Within an IC the basic active element is a transistor (bipolar or FET) and all such devices act as inverters with one or more inputs to create a NAND or NOR gate as the minimum element.

Creating a non-inverting gate such as an AND or OR gate requires additional devices to invert the signal at the input or output of an inverting gate.

Your SR latch would function but would require more transistors than one made of basic inverting gates. It would also be slower and use more power.