By Alex Kirby
Religious affairs analyst
The Pope with former Archbishop of Canterbury Dr Robert Runcie
The worldwide Catholic church has a billion members, the Anglican communion about 70 million.
Numbers aren't everything. But not surprisingly, archbishops of Canterbury are comparative lightweights in inter-faith relations.
There is common ground between the two churches, and for years they have been trying to find ways of showing a more united face.
During the pontificate of John Paul II there has been progress. But it is less than many in both churches have been hoping for.
One seasoned religious commentator, Clifford Longley, writing in the Guardian, said of the Pope: "He was not intolerant of other faiths and creeds, always willing to give visiting Anglican or Orthodox dignitaries a welcome.
"He twice led multi-faith pilgrimages to Assisi. But he left relations with other Christian camps in some ways less hopeful than before.
"The rigour of his theology was too harsh: if the Catholic church was right, the others must be wrong."
Prebendary Dr Paul Avis is general secretary of the Church of England's Council for Christian Unity.
He told the BBC News website: "The Vatican's official position hasn't changed during these 26 years. It has a number of bottom lines, and they're all still in place.
The Pope addresses the Canterbury Cathedral Anglican congregation
"It still doesn't recognise the validity of Anglican orders (the ordained ministry of bishops, priests and deacons) or of the service of the Eucharist.
"And it still regards Anglicanism as something that began 450 years ago, at the Reformation, and not as a church dating back to the start of Christianity.
"Despite that, there's been evident progress in some areas. The Anglican-Roman Catholic International Commission (Arcic) has continued its work.
"Another body, the International Anglican-Roman Catholic Commission for Unity and Mission (Iarccum), is working on a summary of dialogue between the two churches over the last 30 years.
New problem areas
"And I'm sure local unity, at town and parish level, is very much stronger, because Catholics have become full members of bodies like Churches Together in Britain and Ireland.
"They couldn't have got involved unless the Vatican had given its blessing.
"There are two new problem areas, though. Rome made it clear the decision by the Church of England to ordain women as priests was a further obstacle to closer relations.
"And it has serious concerns over the ordination of an openly gay man as bishop of New Hampshire in the US, though it has been reassured by the Anglican Communion's proposals for dealing with the situation.
"So at the personal and pastoral level, there's often a very good relationship. But I think Anglicans remain disappointed there's been no movement on recognising our priesthood, or the validity of our Eucharist."
At a time when both churches face problems in persuading the world they have something to offer, that is hardly a ringing endorsement of their love for one another.