Pulis' second stint in charge of the Potters came to an end last summer, when he left the club by mutual consent.
Beginning in 2006, it saw him guide the Staffordshire outfit into the top flight in 2008 and to respectable finishes in the division around mid-table each season thereafter, as well as the 2011 FA Cup final and the last 32 of the Europa League in 2011/12.
While his successor Hughes has brought in some new signings, most of Stoke's current squad worked under Pulis, who became Palace boss in November.
Hughes said: "We have probably got a unique insight into how Tony sets up his teams.
"You would say that, given the personnel that are still here, they will have a better understanding than most opposition that Tony will go up against with his new team.
"That could be an advantage, but obviously he'll have an insight into what we are doing.
"We are trying to change somewhat, but certainly he'll know the individuals involved and their strengths and weaknesses, so it is an interesting battle of wills."
Hughes is trying to implement a flowing style of football at Stoke, but has been keen to pay tribute to the work done by Pulis at the club.
"The group of players here are a credit to the work that had been done before - the quality of the players in terms of their attitude to work and their application on a daily basis is first class," Hughes said.
"That comes from having good standards within the club, and that happens over a period of time.
"So certainly that influence from Tony Pulis is very evident in the group I work with."
Hughes has little doubt that Stoke fans will also be eager to show their appreciation on Saturday for Pulis' efforts during his Potters tenure - at least until their focus switches to the action of the match.
"I'm sure the vast majority of them will give him a huge welcome," Hughes said.
"But I think the focus will very quickly turn to supporting Stoke and getting behind us like they always do.
"They always travel in great numbers for us and they will be totally behind everybody with a Stoke shirt on.
"They will recognise the work and effort that Tony put into the club, but very quickly move to cheering their team on, I'm sure."
Palace have so far played nine league matches under Pulis, winning three, drawing one and losing five, with the last victory coming on Boxing Day.
They are bottom of the table, a point adrift of safety, ahead of the visit to Selhurst Park of Stoke, who are 12th and without a win in their past four top-flight fixtures.
Stoke striker Kenwyne Jones will not be involved in the encounter as a result of his refusal to play against Liverpool last weekend.
Hughes has decided Jones, who has been fined two weeks' wages, should not be considered for selection, but he will include a new frontman in his matchday squad in John Guidetti, recruited on loan from Manchester City this week.
Another loanee, winger Oussama Assaidi, is available having been ineligible to feature in the 5-3 defeat to his parent club Liverpool, and Jack Butland is set to continue in goal after playing his first full top-flight match on that occasion.
Asmir Begovic, Robert Huth, Andy Wilkinson and Matthew Etherington miss out due to injuries.