The ex-Everton manager was picked by Sir Alex Ferguson to take the reins at Old Trafford following the 71-year-old's decision to retire from management at the end of last season.
Ten games into the Premier League campaign, Moyes's United side currently sit eighth in the table, while Arsenal reside eight points above them at the top of the standings.
"My relationship with Sir Alex will be a bit more peaceful and a bit more serene," Wenger said in a press conference. "It's too early to tell the difference under Moyes. He has shown great competence at Everton."
The two sides will go head to head at Old Trafford on Sunday.