The Celtic striker has been linked with a return to Easter Road this summer with his former club said to be in pole position if the Parkhead side don’t take up an option for another year.
Griffiths worked under Brown during one of his spells with his boyhood club.
The experienced coach reckons the striker has the same ability when it comes to striking the ball as Hearts legend Robertson.
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“All through his career Leigh’s guaranteed you goals”, Brown told the Daily Record. “He’s such a great striker of a football.
“I worked with John Robertson at Hearts who I had always said was the best striker of a ball I ever knew but then working with Leigh at Hibs I would say he could match wee Robbo.
“You knew when they struck a ball it was going to be in and around the goal and with Leigh that could be from any distance.
“He is so good with free kicks too which is such an important part of the game."
Brown believes Hibs would be pulling off quite the coup to bring him back for another spell at Easter Road.
He said: “When Leigh went to Celtic, I thought if he played every week of any season he’d get 30 goals. If he played every game for any club in Scotland he would be top scorer.
“So if he was to end up back at Hibs it would be a fantastic signing.”