Both methods can produce crisp chicken. They create different contact patterns and demand different attention.
Shallow frying
Shallow frying uses less oil and allows easy visual inspection, but the chicken contacts the pan and must be turned. That contact can create darker spots and may damage a fragile coating. Oil depth should still be sufficient to transfer heat around the lower portion of the piece.
Deep frying
Deep frying surrounds the food more evenly and reduces direct pan contact. It requires more oil, more headroom and careful control of displacement and bubbling. A deep fryer may provide steadier thermostat control than a stovetop pot.
Choose by cut and equipment
Small boneless pieces and thinner cutlets can work well shallow-fried. Thick bone-in pieces benefit from more even surrounding heat, but only when the vessel and oil volume are safely sized.
Do not improvise around safety
Never overcrowd, never add icy food and never leave hot oil unattended. The best method is the one your equipment can manage predictably.