While General Liability (GL) and Professional Liability (PL), commonly referred to as Errors & Omissions Insurance, share some similarities, they are for very different reasons. The recommendation for any business owner who needs Professional Liability would be to also carry a General Liability insurance policy.
Both GL & PL are designed to protect the insured from various claims made against them for both actual and alleged wrongs. Both include coverage for attorney fees and both are designed to take the brunt of financial burden from your business should you be found liable.
General Liability insurance is more designed towards physical injury and property damage resulting from your faulty work. As an example, if a customer of yours visits your office on a frosty winter day and slips on the deck in front of your office, you could be held liable for their injuries as you should have ensured safe access to your office.
Professional Liability (E&O Insurance) covers negligence also, but for advice or services provided such as selling an insurance policy. Professional Liability claims are more directed towards financial losses incurred versus physical injuries.
The best way to protect your insurance agency would be to carry both GL and Errors & Omissions Insurance.