The author of Best practices for DNS forwarding [petri.com] recommends using the ISP's DNS servers as forwarders instead of doing the recursive lookups yourself, the main reason being performance. This makes sense as you're only doing one query, getting the response probably right away, given a big enough cache at the ISP and a popular enough website.
A downside of using your ISP's DNS servers might be their stability. It used to be the case that ISP's often had not-very stably DNS servers. However, this can be solved by simply forwarding to name servers such as 22.214.171.124, 126.96.36.199, or 188.8.131.52.
What are the benefits of doing the lookups yourself?
Edit: Using public name servers like Quad9 also adds in security as it filters out known malicious domains.