Fuji hakone pass

I have a JR pass and plan to travel from Shunjuku to Kawaguchiko and then back to Hakone and Tokyo in 2 days.

Which one is suitable between Fuji hakone pass and Hakone free pass? In my opinion, I think it'd be better to buy Hakone free pass which is 3900 yen + highway bus from Shinjuku to Kawaguchiko (1700) + Fujikyu Bus from Kawaguchiko to Gotemba (1470). Therefore, I have to pay 7070 yen for all that is less than 7200 for Fuji hakone pass.
Am I right? Do you have any comment or suggestion for this issue?

You forget the train ride from Hakone back to Tokyo. With that included, the Fuji Hakone will come cheaper.

If the original poster has the JR Pass, then isn't that good to cover the way back from Odawara to Tokyo/Shinjuku covered? (with the rides from Gotemba around Hakone down to Odawara covered by the Hakone Free Pass)

Sorry, I did not notice that Dinon is using a Japan Rail Pass. In that case, it is cheaper to go with your suggested tickets instead of the Fuji Hakone Pass. To save a further 600 yen, you should take the JR limited express train from Shinjuku to Otsuki (fully covered by the Japan Rail Pass) and catch the Fujikyu Railway from Otsuki to Kawaguchiko (1110 yen, not covered).

Thanks for your answers.