Well, I agree with all the above, but particularly with pjt33, in the sense of "funny" having a wider range of meaning and meanings. Because while in the primary sense of, "providing fun; causing amusement or laughter; amusing; comical"
a funny remark; a funny person, you could also say
an amusing remark; an amusing person... in a second sense of funny as "attempting to amuse; facetious"
Did you really mean that or were you just being funny?, I do not think you could say here
"or were you just being *amusing". You could say
or were you just being facetious (gracioso, burlón). Besides that, "funny" has other meanings and usages that "amusing" does not have. For example, in the sense of "warranting suspicion, deceitful", as in,
We thought there was something funny about those extra charges. (Pensamos que había algo raro con esos honorarios/precios adicionales/extra) No sería "divertido" ni "gracioso" a no ser que estuvieras siendo muy irónica.
Also "funny" has a sense of "insolent; impertinent" as in,
Don't get funny with me, young man! Which in Spanish you can use "gracioso" in the same sense,
¡No te hagas el gracioso conmigo, jovencito! (No te me pongas impertinente...) You'd never use "amusing" in such context and such concept.
Then again, "funny" has a sense of "strange, curious, peculiar, odd,
the funny thing is that … lo
extraño or
curioso del caso es que …;
she speaks with a funny Westerner’s twang habla con el acento nasal
rarito del Oeste de los Estados Unidos.
In the case of using "amusing" in these contexts, the word "amusing" would have the literal meaning of "divertido, gracioso" and not so much the clear sense of "odd, peculiar" that funny has.
Funny has synonyms like, comic, farcical, ridiculous, humorous... (gracioso, cómico, divertido) (Then, raro, extraño, curioso) (Also "medio mal/chungo" as in "I feel funny", as in a little bit ill. In Spain you would also say "no estoy muy católico/-a".)
Synonyms of "amusing" would be "entertaining, charming, cheering, lively"...
Well, I hope my disertation is not too long and boring, and if it is not funny and amusing enough... you could attribute it to the fact that the one who wrote it... well
he’s a bit funny in the head (está medio tocado [del ala]) (A context were you would never use "amusing")

(Unless you really wanted to "amuse" your readers!!!)