Worth, value are close synonyms in more than one of their senses, often differentiated by demands of idiom rather than differences of meaning or connotation.
Both worth and value denote the equivalent in money or sometimes in goods or services given or asked in exchange for another thing; thus, the value or worth of these coins to collectors is much greater than their monetary worth or value .
When, however, worth and value mean the quality of being useful, important, excellent in its kind, or highly desirable or meritorious, they do not always come so closely together. In such use worth more often than value applies to what is excellent intrinsically (as by being superior morally, spiritually, intellectually, or aesthetically).
Value , on the other hand, applies more frequently than worth to the qualities (as excellence, usefulness, or importance) imputed to a person or thing or to the degree in which that person or thing is regarded as excellent, useful, or important especially in its relation to other things.
Further, value may be applied, as worth is not, to something (as a principle, a quality, a condition, or a substance) which is regarded as important, useful, desirable, or of value, sometimes in its relation to other things, sometimes in the degree which seems proper or fitting to it, and sometimes absolutely.