The two captains fell out when England won the series in South Africa four winters ago over an incident which ended with Vaughan being fined his entire match fee after criticising the umpires for their handling of bad-light issues in Johannesburg.
But their rivalry goes back further than that. Smith was in charge here five years ago and the left-handed opener scored his second double-century of the 2003 series at Lord's - Vaughan's first in charge, which the visitors won by an innings.
Plenty of water has flowed under the bridge since both those battles, though, and Vaughan may need to be at his tiptop best, as captain and batsman, to prevent South Africa from winning their first Test series over here since being readmitted to world cricket in 1991.
"This is a tour we have been talking about for a long time," said Arthur after South Africa's final warm-up match, against Middlesex at Uxbridge, was washed out.
"Just training at Lord's the other day there was a special buzz. We have not won here since unity [the post apartheid era] so it's something we've put high on our agenda."
Although South Africa were fancied to do well before their three previous series in England - they drew in 1994 and 2003 but lost in 1998 - these tourists are favourites to win. And that can bring extra pressure.
"I believe the guys deserve to be tipped, but really that counts for nothing. It's about how we bat and bowl in the series," said Arthur.
"I think England are in a slight transition period, probably where we were a year ago in terms of the make-up of their side, getting their combinations right and bringing new faces in.
"But they are a very good Test team and will take a lot of beating. We will need to play very well."
Although Arthur's batsmen have done most to catch the eye against first Somerset and then Middlesex, it is their fast bowling unit that keeps making the headlines as Makhaya Ntini, Morne Morkel and Dale Steyn are all 90mph operators.
But while 30-year-old Ntini has bags of experience, Morkel and Steyn are still learning their trade.
"I think the sight of Steyn and Morkel is going to be something special this summer," said Arthur. "They are young and they haven't been tested with all this hype before, but I'm pretty sure they will be fine.
"And they will never get over-confident, there's no chance of that."
