Obstinate, dogged, stubborn, pertinacious, mulish, stiffnecked, pigheaded, bullheaded are comparable when they mean fixed or unyielding by temperament or nature.
Obstinate implies persistent adherence, especially against persuasion or attack, to an opinion, purpose, or course; when applied to persons or to their ideas or behavior the term often suggests unreasonableness or perversity rather than steadfastness.
Dogged adds the implication of downright and tenacious, sometimes sullen, persistence; usually, also, it connotes great determination or an unwavering purpose.
Stubborn is often used interchangeably with obstinate and dogged, for it implies the unyielding adherence of the one and the tenacious determination of the other; more strongly than either of them, however, it carries an implication of a native fixedness of character or of a deeply rooted quality that makes a person sturdily resistant to attempts to change his purpose, course, or opinion, or that makes a thing highly intractable to those who would work it, treat it, or manipulate it.
Pertinacious lacks, as compared with obstinate, the implication of resistance, and as compared with stubborn, the suggestion of inherent quality; it usually implies a chosen course and stresses its pursuit with stick-to-itiveness and, often, with a persistence that is annoying or irksome.
Mulish suggests an obstinacy as characteristic or as unreasonable as that of a mule.
Stiff-necked , more even than obstinate or stubborn, stresses inflexibility; it often also suggests a haughtiness or arrogance that makes one incapable of respecting the commands, wishes, or suggestions of others.
Pigheaded and bullheaded suggest a particularly perverse or stupid kind of obstinacy; therefore they are chiefly terms of severe reproach; pigheaded, however, often suggests impenetrability to argument and bullheaded, headstrong determination.