If these teams had met in this final just 13 years ago, Swansea would have been the fourth-tier outsiders taking on top-flight opposition such have been the contrasting fortunes of the two clubs over recent years.
Giant-killers Bradford, who have already trampled over three Premier League teams in Arsenal, Wigan Athletic and Aston Villa to book only their second Wembley appearance, are hoping for another upset. Swansea have a one-word reply in the shape of Spanish striker Michu.
Michu is in prolific form with 18 goals in all competitions, including the 15 that have propelled the Welsh side to eighth place in the Premier League, and he is not about to let Bradford get in his way of silverware.
"We are determined not to let the underdog win," he said on the club website.
"We have had a fantastic season in the league, so to win a first major trophy for the club as well would make it even better.
"That would also mean European football for us next year, and that has always been a dream of mine."
Sunday's winners will earn a place in the Europa League, the continent's second tier club competition, and the idea of Bradford taking part will seem to many even more preposterous than this Wembley encounter.
The West Yorkshire club have endured some torrid times of late with two periods in administration following their 2001 relegation from the Premier League, while the tragedy of the 1985 fire that killed 56 fans at their ground lives with them.
Unlike Swansea, Bradford have a major trophy to their name in the 1911 FA Cup but it will be this season's battling displays that will inspire them on Sunday rather than the feats of a generation long gone.
"We've got nothing to lose and everything to gain," Bantams manager Phil Parkinson told reporters.
"The bookies have written us off, they have done in previous rounds. When you look at the league positions you can understand that.
"It's a two-horse race, one of the horses is an overwhelming favourite but in a two-horse race anything can happen on the day. In the previous rounds Lady Luck has played a part for us but also incredible desire and spirit in the team."
The only other time Bradford have played at Wembley was in the 1996 third tier playoff against Notts County, which they won 2-0, while Swansea's most recent appearance was a 4-2 win over Reading to earn promotion to the Premier League in 2011.
Neither team are going into the final with good results behind them with Swansea manager Michael Laudrup resting a host of regular starters in a 5-0 thumping by Liverpool last weekend while Bradford lost 2-1 to AFC Wimbledon.
While the League Cup lacks the prestige of the FA Cup, with top clubs often opting to field experimental sides especially in the early rounds, for the players who take to the pitch on Sunday this trophy means everything.
For Bradford, whose players are still pinching themselves that it is even happening, the day itself is big enough.
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