I'm a son of both denominations. I am an Anglican who studied in a Wesleyan setting for the first few years of my training. I believe the "scriptural holiness" message as well as the teachings of Anglo-Catholicism. That would put me pretty much in the same boat as Charles Wesley.
Having said that, I would argue that the Anglican distinctives are still best summarized by the Lambeth Quadrilateral (which I am not terribly interested in these days) which was formulated well after the Wesleyan revival (1888)
- The Holy Scriptures of the Old and New Testaments, as "containing all things necessary to salvation," and as being the rule and ultimate standard of faith.
- The Apostles' Creed, as the Baptismal Symbol; and the Nicene Creed, as the sufficient statement of the Christian faith.
- The two Sacraments ordained by Christ Himself - Baptism and the Supper of the Lord - ministered with unfailing use of Christ's words of Institution, and of the elements ordained by Him.
- The Historic Episcopate, locally adapted in the methods of its administration to the varying needs of the nations and peoples called of God into the Unity of His Church.
However, these are generally interpreted by Anglicans as being deliberately broad and various parties within Anglicanism add and interpret these points according to their emphasis. For example, an Anglo-Catholic would add five more sacraments etc. Get more info here:
http://www.acahome.org/tac/library/docs/quadrlat.htm
One point I would hasten to add is that nowhere is communion with Canterbury seen as an essential to Christian Faith in the Anglican Tradition. This is where Rome and Canterbury depart and where Canterbury seeks to walk closer to the East. Today there are around 1 million Anglicans in suspended or impaired communion with Canterbury, mainly over the modern day issues of who is eligible for ordination and church discipline.
Because Anglicanism is born out of an autocephalous national church, true Anglicanism is really "Christianity as practiced in the English tradition". Hence, Anglicanism really takes with it everywhere that liturgical and dogmatic culture that defined England and its missions abroad for centuries. This is where the broad diversity comes from. Today, the churches abroad march to their own drum in many ways, and this further increases the diversity. For many, the See of Canterbury is the seat of unity amidst this diversity, but none think it essential for the Faith to thrive and be salvific.
The Wesleys and other founding methodists could sit easily within the boundaires of the Church of England, but church politics played a prominent role in those days and perhaps the Church of England could not stomach the creative spirit and inspired brilliance of the Wesleys, and thus made the cracks which would needlessly divide the two in future generations.
Let's just love each other and maybe one day the cracks will be healed.