The Hammers parted company with Allardyce back in May after four years in East London.
The football West Ham reverted to in the second half of last season was typical of an Allardyce outfit, and many Hammers fans were disenchanted with what they were watching.
Just three wins in the entirety of the second half of the season ultimately cost Big Sam a new deal, and Bilic was brought in to replace the experienced former Newcastle United man.
His replacement has started his debut Premier League season as a manager in great form, with the Hammers sat sixth in the table with 14 points from the first eight games.
They have beaten Arsenal, Liverpool and Manchester City away from home and are the joint-second highest-scoring side in the league.
Meanwhile, Allardyce has now called time on his five-month break from football after accepting a job as Black Cats boss last week.
'The football is far better to watch this season'
And Sullivan has wasted little time in taking a shot across the bows in the direction of the Stadium of Light in his column on West Ham's official website, saying Bilic has brought the X-factor back to Upton Park.
"This has been an impressive start to the season and we hope to keep our unbeaten run going when we head to face Crystal Palace on Saturday," Sullivan told whufc.com.
"The football is far better to watch this season and it's great to see goals.
"People are starting to call us the entertainers as we are such high goalscorers, with goals coming from so many different players.
"Let's hope the goals keep coming and our reputation for playing entertaining football again continues."
Hammers chief scratching an itch?
You get the impression Sullivan has been itching to get that off his chest, but was biding his time until he felt the moment was right.
With Big Sam back in the Premier League, and West Ham having got one of their games against his new side out of the way last time out, now seems as good a time as any.
Undoubtedly Allardyce would not agree with Sullivan's assessment, we all know how proud the Dudley-born boss is of his extensive CV.
Attacking football wins admirers
But it is difficult to argue with Sullivan, and the proof is very much in the watching.
Under Big Sam, West Ham barely attacked away from home, the boss happy to sit back and play for a draw more often than not.
But now, with the likes of Dimitri Payet and Manuel Lanzini thriving in Bilic's attacking system, the Hammers go at teams regardless of where they are playing or who they are competing against, and that approach has already reaped handsome rewards.