I am not familiar with WebInspect, but i use burp pro every day, and the more i rely on it, the more features i discover (even after multiple years of use).
It is so much more than only a proxy. You can actively or passively scan webapplications, compare requests, use the intruder to perform brute forcing, it even has a compare function for sessions to check for randomness in the received session identifier. Heck, it even helps you spider the website, and if you use the active scanner it will find sql injections, xss, path traversals etc. so you can even use it as an automated tool.
CISSP, CEH, ECSA, OSCP, OSWP, eCPPT, eWAPT
earning my stripes appears to be a road i must travel alone...with a little help of EH.net