old vs not bad

old is a noun but not bad is not a noun.

Word	Noun	Adjective	Verb	Adverb
old	Yes	Yes	No	No
not bad	No	Yes	No	No

As adjectives, old and not bad are synonyms defined as:

Other synonyms of old include bang-up, bully, corking, cracking, dandy, great, groovy, keen, neat, nifty, peachy, slap-up, smashing, swell.

old (noun)	not bad (noun)
past times

old (adjective)	not bad (adjective)
of long duration; not new	excellent
(used especially of persons) having lived for a relatively long time or attained a specific age
skilled through long experience
(used for emphasis) very familiar
excellent
just preceding something else in time or order
belonging to some prior time