follow vs following

The choice between follow and following is subjective. Either could be used and be correct.

Although if following were used, the sentence would need to be rephrased in order to drop to be:

There is no greater thing than following your passions in a way that serves the world and you.

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The conjugation of to serve has nothing to with passions.

The following subject is what determines the singularity or plurality of the verb:

in a way that serves
in ways that serve

In comparatives like greater...than, the nature of the word after 'greater' and 'than' should be similar.
For example, "Better live than die"; not Better you live than dying.

The saying is "Better a living beggar than a buried emperor"

Here, it is wrong to say, 'Better live a beggar than a buried emperor."

"That serves the world and you" is a restrictive relative clause with "that" being the relative pronoun representing "the way," which is singular. "Serves" agrees with "that," because "that" is a stand-in for "the way."

Both follow and following work fine. What's interesting is that "follow' is an infinitive that has dropped its "to," which accords with the following

An infinitive can also lose its to when it is the second (or third, fourth, etc.) item in a series. For a series of infinitives, you need only the first to. The rest are unnecessary. http://www.chompchomp.com/terms/infinitive.htm