Is it recommended to fill the "Online Presence" in the online ESTA application?

According to CBP official website FAQ on the Visa Waiver Program Improvement and Terrorist Travel Prevention Act Frequently Asked Questions, the question is completely optional.

Do I have to answer the new questions if the provisions of the new Act do not apply to me?

Yes. All ESTA applicants must complete all non-optional fields on the ESTA application.

The social media question is optional. The ESTA application will clearly inform the applicant that answering it is optional.

and also

How will CBP use my social media information collected through the additional questions being added to the ESTA application in October 2016?

Information found in social media will enhance the vetting process and may be used to review ESTA applications to validate legitimate travel, adjudicate VWP ineligibility waivers, and identify potential threats. If you choose to answer these questions and an initial vetting by CBP indicates possible information of concern or a need to further validate information, a highly trained CBP officer will have timely visibility of the publicly available information on those platforms, consistent with the privacy settings the applicant has chosen to adopt for those platforms, along with other information and tools CBP officers regularly use in the performance of their duties.

For example, social media may be used to support or corroborate a traveler’s application information, which will help facilitate legitimate travel by providing an additional means to adjudicate issues related to relevant questions about identity, occupation, previous travel, and other factors. It may also be used to identify potential deception or fraud. Social media may help distinguish individuals of additional concern from those individuals whose information substantiates their eligibility for travel.

DHS will handle social media identifiers in the same manner as other information collected through ESTA. DHS has documented these procedures in the updated ESTA System of Records Notice (SORN) and Privacy Impact Assessment (PIA), which are available on the DHS website (http://www.dhs.gov/topic/privacy).

And to answer your questions...

What are the pros and cons of filling the "Online Presence" field?

• Pros: Information found in social media will enhance the vetting process and may be used to review ESTA applications to validate legitimate travel, adjudicate VWP ineligibility waivers, and identify potential threats. Social media may help facilitate legitimate travel by providing an additional means to adjudicate issues related to relevant questions about identity, occupation, previous travel, and other factors.

• Cons: none, except they can look into your social media.

Are there any situation where it is a good idea to fill it?

Yes, if you have nothing to hide and do not mind sharing your social media with CBP for investigation into your background. It can help verify your intention of travel and your legitimacy, completely at your discretion.