The first ever encounter between Dyab Abou Jahjah, president of the Arab European League, and Tariq Ramadan, 'the preacher of the banlieues'. was a gladiatorial but good-humoured affair. In front of a surprisingly mixed audience at Erasmus University, two possible futures for Muslim politics in Europe came face to face. But do they represent the twin unacceptable faces of European Islam – the clerical and the radical – best avoided? Or are they, to invoke a comparison made on the night, like Malcolm X and Martin Luther King, people with constituencies and convictions, with whom we should be allying ourselves in the fight against religious extremism and political violence? Both figures can claim to have headed off rather more religious fanaticism in Europe than most of us: Ramadan in taking on the anti-Semites, Salafis and literalists in the Muslim world, and Abou Jahjah for preventing young people in places like Borgerhout, the Moroccan district of Antwerp, from falling prey to extremist networks. So could they be friends? Our friends? And which would be the better ally?

Both have been dogged by their share of controversy. Ramadan, the Swiss-born grandson of the founder of the radical Muslim Brotherhood, secured a good teaching job at Notre Dame University, only to be denied a US visa (something he is contesting in the courts). Meanwhile the philosopher and mediator was invited to be on Tony Blair's post 7/7 task force: he resides in the UK, a visiting fellow at St Anthony's Oxford.

By contrast Abou Jahjah, Lebanese by birth, is a political activist living in Antwerp (a famously divided city he describes as 'neurotically racist'). Deeply engaged in local resistance against racism, he founded the Arab European League and Belgium's Muslim Democratic Party. Jahjah positively courts controversy. The AEL's response to the Danish Cartoons has been to publish a series of viciously anti-Semitic cartoons on their website, as well as a cartoon mocking Dutch MP Ayan Hirsi Ali and her campaign against female circumcision – an attempt, they claim, to expose the hypocrisy surrounding the issue.

Both Ramadan and Abou Jahjah regard themselves as part of, and leaders in, the Muslim community: they just have polar opposite positions on what this means. Abou Jahjah sees himself as part of a pan-Arab nation or diaspora, which finds itself in Europe because of colonialism, fighting oppression; while for Tariq Ramadan the quest is how to be fully European and fully Muslim at the same time, where Europe is an inspiration for a renewal, an Islamiic reformation.

For Abou Jahjah the task is to change Europe: "Why do people take it for granted that we should look at the Netherlands, France and Belgium as places where we should just fit in? When we see that they do not live up to their own constitutions, or EU or international conventions on human rights – shouldn't we be changing them?" For Ramadan it is for Muslims to fully occupy their status as European citizens, claiming the rights this grants, including the right to live as a Muslim.

Abou JahJah and Ramadan hold views that liberal humanists would find unacceptable, but both evade easy categorisation; and the way in which they comfortably use the terms of western liberal discourse makes them hard to simply dismiss. Take Abou Jahjah on theocratic authoritarianism in Islam: "When an exclusive group takes to itself power to issue fatwas over and above society…[T]his concentration of knowledge is as antithetic to a healthy democracy as any concentration of capital." Two years ago the AEL survived a challenge from its then strong Islamist wing. This resulted in a new vision statement rejecting any kind of theocratic state: "The bottom line for us was always democracy." Islam remains central to the symbolic and cultural identity of many AEL members, but is regarded as having no theological or political repercussions. The AEL clearly declares itself a multi-confessional campaign, containing Christian Arabs, Jews and those of no religion. It focuses instead on the notion of Arab as a cultural identity, an identity intimately wrapped up with a history of struggle.

But for Ramadan, nothing is more calculated to exacerbate a 'victim mentality' amongst Muslims living in Europe, aiding European society to treat Muslims as a minority apart. This 'victim mentality', Ramadan says, can be so easily manipulated by an 'ideology of fear' avidly seeking the next 'fifth column', the enemy within. He is utterly opposed to Islamic schools, Islamic political parties and affirmative action of the kind that the AEL espouse. For Ramadan the task is to contribute to a new definition of pluralist, democratic belonging: "The worst mistake that you could make," he urged the 880-strong audience in Rotterdam, was to be obsessed with "your minority status as Muslims."

There was no such thing as minority or second-class citizenship in Europe. "If someone refuses me a job because my face looks like an Arab face, I can give up, saying, 'OK – He doesn't like Islam!' or I can say, 'There are laws in this country, and I will act against all forms of discrimination because racism is a danger to our society and to our future. So by exposing your malpractice, I am helping to improve this society for everybody." Muslims in the audience should believe that they are 'at home' and make a contribution. For his part, Dyab Abou Jahjah regards this preoccupation as a form of 'creeping assimilation'.

Take the choice, for example, between British multiculturalism and the French Unity of the Republic. Ramadan thinks neither adequate, but begins from the premise that, "it is simply not sustainable to live with this notion that as citizens we differ more than we have in common." Abou Jahjah starts from a refusal "to give up what makes you different." Calling for a 'multiculturalism that works', he is engaged in a concerted attempt to oppose what he sees as a European project of monocultural assimilation.

Of course these are not the only possible futures for European Islam – there are others: some, as we already know, potentially deadly. But we cannot afford to ignore any of them, especially those that stand against terror.