The Tigers have had a fairly good start to their Barclays Premier League campaign and currently sit two points ahead of West Ham in the table, with Allardyce admitting he has been suitably impressed.
"For them to get their first away win was a huge result, it lifts the whole city, the backroom staff and all the players," he said.
"We face them at a time when their confidence is sky-high so as always we'll have a tough game on our hands.
"His [Bruce's] players, irrespective of how many he's changed, have gelled well which was the opposite to his time at Sunderland.
"At Hull he's changed a lot of players and it's worked for him very, very well in a short period of time and they've obviously started the season exceptionally well."
West Ham's own victory last weekend saw them bring to an end a barren run in front of goal.
Highly-rated midfielder Ravel Morrison has continued to impress since working his way in to the team and Allardyce believes the former Manchester United youngster is playing well enough to maintain his place.
"At the moment his performances are exceptionally good and that means you don't have to fight for your place," said Allardyce.
"If you're good enough then you're old enough and he's proved that up to now. We've got to keep his feet firmly on the ground and watch out for head swelling."
Despite breaking their goalscoring duck against Everton Allardyce remains keen to strengthen his striking options in the wake of Andy Carroll's pre-season heel injury.
Mladen Petric was signed on a free transfer and former Hammer Carlton Cole will soon join him once Allardyce is convinced by the England international's fitness.
"We've had Carlton training with us for a while now and as soon as he's fit enough to play there will be an offer of a short-term contract on the table, there's no doubt about that," he confirmed.
"That's why he's here with us and that's why we're trying to improve his fitness having missed pre-season. As soon as he's okay and suitable terms and conditions have been agreed, which is nothing do with me, then he'll join us for however long the contract is negotiated for.
"We'll play a couple of behind-closed-doors games just to let him get some match practice and then we'll take it from there."