Yet as far as one group of people is concerned, they might as well be a million miles apart. In a dispute extraordinary for its viciousness but in its sentiment all too common in middle-class Britain in 1996, parents are determined to do everything they can to ensure that their children have more chance of going to one school than the other.
Their campaign has seen letters forged, anonymous angry leaflets circulated, and a bemused county council swamped by well-orchestrated letters from as far away as Kent, Nottingham and Norwich. Complaints from people that their names had been falsely used and their signatures faked have forced the council to consult lawyers and consider calling in the police.
The battle has spilled on to the pages of local newspapers, with Conservatives accusing the Labour-Liberal Democrat council of not listening to local people. Labour and the Lib Dems blame the Tories for fuelling the war and not strongly condemning the underhand methods being used.
The identity or identities of the forger may never be known. What is certain is that he or she feels so strongly about the county council's plans for the schools that they have resorted to a strategy rarely seen in Britain's town halls, let alone in sleepy, affluent Hertfordshire. What should have been a straightforward decision to increase the size of a primary school to cope with new housing development in a suburban backwater has taken on a sinister face.
It began quietly enough. In May, Hertfordshire council issued a public consultation document about its plans for the primary schools in West Cheshunt. More than 1,000 new homes were planned for the area and two options to boost the number of necessary school places were on the table: give all of them to Fairfields or share them between Fairfields and the larger Andrews Lane.
Historically, Fairfields enjoys the better reputation, is located at the smarter end of Rosedale, is always heavily over-subscribed and gets more of its pupils into Goff's, the local selective grant-maintained secondary.
Andrews Lane, though, has a new head and is on the way up. The council declared its preference for the second option, to give both schools a lift and not to be seen to prefer one over the other. Public meeetings were held at both schools. Parents at Andrews Lane were happy with the council's preference. Their meeting was attended by 75 people and passed off quietly.
The first inkling of trouble came with the later, Fairfields meeting. Before it, an unsigned circular appeared: "Fairfields School - the best for expansion, the best for admissions, the best for locality, the best for pupils, the best for the future."
More than 200 people attended - some of whom, it was noticed, had also been at the earlier St Andrews meeting. Speaker after speaker condemned the council and its education planning officer present, Stuart Freel.
Letter after letter began arriving at county hall. In all, officials have received 436 in favour of giving all the places to Fairfields.
Many have the same wording and have been produced on the same word processor. That, officials say, is not unusual - such public consultation exercises often result in people signing letters drafted for them. But, they say, such a large number is rare, as are those from addresses well away from Cheshunt.
What is unheard of, said Jan Beavis, an education planning manager at Hertfordshire council, is the file of letters marked "Of Doubtful Origin". It contains 18 letters, for some of which, when the council replied acknowledging receipt, the Post Office found either no trace of the address or anyone of the signatory's name.
Then there are the letters such as those from Mrs A of Cheshunt and Mrs J from Norwich. Mrs A's letter says she has just moved to the area and would like her daughter to go to Fairfields. "I, as a local resident, want the taxpayers' money spent on option A [to give all the places to Fairfields] to make Fairfields an even better school than it is now."
When Mrs A received the council's acknowledgment of the letter, neither she nor her husband knew anything about it. She wrote to Mr Freel: "The signature on the fraudulent letter is not mine and was done without my knowledge or consent. I am an officer of a bank and hold authorised signature powers, and any fraudulent use of my signature is a very serious matter. Please urgently investigate this item and let me know the outcome."
From Norwich, Mrs J also complained. She, too, knew nothing about a letter to Hertforshire County Council about a school in Cheshunt. Her signature also had been forged.
Linda Dambrauskas, a Labour councillor, said that Fairfields parents thought that by sending their children to the school they were guaranteed places at Goff's. She did not know who was behind the forgeries, but accused Conservatives of running "an orchestrated campaign".
John Rose, her Tory counterpart, retorted that "parents are understandably fiercely protective of their children's interests". Mr Rose condemned the forgeries, but added: "It is hardly surprising that a few are carried to excess."
In a phrase that his political opponents claim lies at the heart of the issue and explains the Tories' willingness to embrace the campaign, Mr Rose wrote in the local paper: "Can we trust the New Labour-Lib Dem administration at county hall? If we can't, could we trust their colleagues in power at national level? I hope we don't have to find out the hard way!"
This, say the Tories' opponents, is evidence that they are unconcerned about the dirty tricks in an effort to embarrass Labour and the Lib Dems, to claim the county council is behaving in a heavy-handed manner, and to use Cheshunt as part of the forthcoming greater national assault.
So far, Marion Roe, the Conservative local MP, has said nothing about the forgeries - calls to her office were not returned - but her Labour opponent, Ben Coleman, is calling for a full council investigation. "Why does she not condemn it - or is this another example of the Tories going along with sleazy behaviour?" he asked.
The council meets next month to decide formally which option to approve. The letters in the "doubtful origin" file will be discounted. As for the 436, they may also have been in vain. "The decision will be made by county councillors - their decision will not be based solely on the weight of letters," said Ms Beavis.
In the meantime, Hertfordshire police may be asked to penetrate behind the lace curtains of usually crime-free Cheshunt.