Logical, analytical, subtle are comparable when they are applied to persons, their minds, their mental habits, or products of their reasoning and mean having or showing skill in thinking or reasoning.
They are often used interchangeably or without clear distinction, but it is possible to employ them distinctively and with precision.
Logical may imply the power to think according to the rules of logic and therefore in an orderly fashion; more often, however, it suggests the power to impress others that clearness of thought, soundness of reasoning, and freedom from bias underlie one's arguments, one's decisions, or one's policies.
Analytical stresses the power to simplify either what is complex or complicated (as by separating it into its constituent parts) or what is chaotic or confused (as by reorganization that shows the relation of the details to each other and the whole). In derogatory use it may imply a tendency to multiply subdivisions but in favorable or neutral use it connotes a power to systematize, clarify, and interpret, as distinguished from the power to create or invent.
Subtle stresses the power to penetrate below the surface and to perceive fine distinctions and delicate, almost imperceptible, relations. When applied to arguments its use may imply a criticism, such as being hard to follow because of being overrefined. Usually, however, it connotes extraordinary skill in reasoning or in analysis.