Both are uncovered stone built arenas that bake in the Mediterranean sun, and which staged some of the greatest spectacles of the ancient world.
Valencia has a more impressive construction than both. Like the others, it's open and multi-tiered, except it's far bigger. The Panathenaic still seats 45,000 and the Colosseum could hold 50,000. Valencia's Nou Mestalla holds even more, except Valencia's arena isn't a Roman relic, but a modern day edifice which started rising from the ground in 2006, only to grind to a halt 1,000 days ago.
The Nou Mestalla project has been "a nightmare" according to Valencia's legendary goalkeeper Santiago Canizares and the current Valencia players are reminded of it every day. Most of them live just over the road in spacious new apartment blocks. The area is not full of bars and restaurants, which is how the club like it. But it is convenient for their training ground 15 kilometres to the north and it will be even more convenient when the new stadium opens.
The players drive past the half built arena each day as the morning rush hour heads into Valencia in the opposite direction.
Most players. Portuguese right back Miguel has slept through too many rush hours. He was in the top five right backs in the world two years ago, but his nocturnal predilections are causing grief for his club. Miguel keeps turning up late for training and is constantly spotted in nightclubs in the early hours surrounded by beautiful women. Valencia's strict Basque coach Unai Emery has lost patience and wants to sell him. Miguel is no example to the others and his tardiness doesn't help team spirit.
Miguel aside, Valencia's players are ultra-professional and they have overachieved in recent seasons with successive third place finishes.
The financial uncertainty which surrounds the club has become the norm. Players know that the team's star is likely to be sold each summer to help with finances. Thankfully, Valencia continues to be a finishing school for some of football's brightest talents. Villa, Silva, Mata, they all starred at the original Mestalla before moving - with regrets - as their club cashed in. Valencia fans hope for the day when they don't have to sell their best players, a day when they can realise their potential.
It's early December in Valencia and one of the few wet days in a city which enjoys over 300 days of sunshine a year. The half-built stadium is a depressing sight and puddles of water form outside what will be the main entrance, but the scale is vast.
North of the city, a café outside the club's training ground hums with conversation from the dozen journalists who cover Valencia and some of the club's coaching staff. Talk in the rest of Spain centres around the clasico, but in Valencia people are concerned with Valencia. Or neighbours Levante, but that's another story for another day.
Valencia fans loathe the obsession with the big two and feel that their past achievements are overlooked: consecutive Champions League final appearances, the title win in 2002 or the league and UEFA Cup double in 2004. Such successes seem a long time ago. Today, Valencia talk centres as much on the club's finances as to what happens on the field.
"Things are a little bit better," opines a journalist from Marca when asked to compare now to 2009 when the club nearly went bankrupt, "but they're still very bad. Valencia still expect to sell a crack — probably Soldado - at the end of the season."
"The club president keeps saying that he's close to doing a deal which will see work re-start on the stadium, but there's a lot of scepticism."
That is understandable. Spain is suffering deep economic problems, specifically in construction, and Valencia's main issue was not being able to sell the valuable land close to the city centre where their old Mestalla home stands. They weren't to know that the property market would crash soon after building started on their new home.
After my trip to Spain's third biggest city of 800,000 at the start of this month, the mood worsened as Los Che were knocked out of the Champions League by Chelsea and beaten in the league by two injury time goals by a Real Betis who just before couldn't buy a win.
Things have improved markedly since then on all fronts. Last week Valencia announced the news that a bank will take care of the land on which the old Mestalla stands. It will be worth a lot of money some day, given that it stands in the middle of a prime residential area. That guarantee means that Valencia have the financial security to restart building of the new stadium and they predict the new Mestalla will be ready in two years.
President Manuel Llorente, who has done much to steady the Valencia ship, said: "It's a landmark agreement, this will make all those hundreds of thousands of Valencia fans happy, knowing that their team will play in one of the best stadiums in the Europe. This new stadium will help Valencia take a leap in quality in all areas."
The future of Valencia is bright and no matter how many world titles Barcelona win or goals Cristiano Ronaldo scores, that's what really matters to fans of Unai Emery's club.