Neither is better outright - forging gives higher strength and toughness, while casting produces intricate shapes with little waste. The right choice depends on the component, the volume and the alloy.
Forging
In forging, a solid item of metal is repeatedly struck by the anvils of a forge to produce a near-net shape, closer to the finished dimensions. Forged components can reach higher strength than cast ones because the microstructure is refined during reduction. The grain structure also tends to follow the shape of the component, giving favourable mechanical properties across section changes. Forging is therefore typical for shafts.
Casting
In casting, molten metal is poured into a mould. Once solidified it can achieve quite intricate shapes with little wasted metal and a reduced need for machining. Casting requires a pattern, from which the mould is fabricated, and this can add significant cost and time. The mould and runner system that carries the molten metal is challenging to design, since it has to allow for shrinkage as the metal cools.
The mechanical properties of a casting are generally much lower than a forged bar, depending on the alloy. Casting is most typical for medium to large runs of the same component, where the volume justifies the cost of pattern and mould making.