I am drawn to Anglicanism for much of the same noted directly above by FormerReformer (when he was Episcopalian, I take it) and some ways back by Doubting Thomas - the Book of Common Prayer (for me, 1928 and preceding versions though I've only browsed the 1662 online), then of course the KJV, and some of the earliest English-language Protestant choral music that (to me, no musician and ignorant of the technical distinctions) retained a good bit of the sombre old Catholic 'feel' like the anthems of Thomas Tallis, William Byrd (incidentally they were both Roman Catholic) and Orlando Gibbons.
Those things, lofty and beautiful, are somewhat superficial. The primary draw is the clear place of Scripture as primary authority, inferred from the heavy quotations of Scripture, arguably Scripture-derived teachings and supposedly (I buy the line but won't defend it against Orthodox or Roman/other Catholic) *only* what can be proved from Scripture. More than anything else, this might be a mere imaginary comfort that I tell myself, because probably every one believes and will rigorously defend things they believe that may make no use of the Bible whatever.
Some years ago it was most important to positively affirm a homosexual identity for myself - and with that, most absolutely the "behaviors" that go with that identity, and I chose to be baptized into the Episcopal church. At the time I still had overall theologically conservative beliefs for a Protestant, and knew of the Spong etc. controversies, but thought the Episcopal Church broad enough that I might grow there. But the briefest fascination there faded, and my beliefs have since gone fundamentalist-ic, as in mostly taking a literal view of the Bible because my simplistic mind cannot well deal with the complexities of where to differentiate literal or allegorical, historical or mythical interpretions. I believe again that homosexual sex acts are sinful so can't use that affirmation for myself to stay in the Episcopal Church, and now look mostly to the Anglo-Catholic parts of the Anglican Continuum, because I still want the primacy of Scripture to stand as a distinctive. If the Scriptures are not primary, then out of the many varied opinions of Church Fathers and modern theologians, any "Church" could theoretically change its values or teachings as on a whim (a broadly social or academic accepted whim).
The historical continuity (and to some extent then, integrity) of Anglicanism is compromised by the current state of affairs in the Anglican Communion, among them the drift (personally I grievously lament it) between moral/socially conservative, low-church Evangelicals who I hear don't even utilize the Book of Common Prayer in worship services, and moral/socially liberal, High-Church Anglo-Catholics. To me as of yet, this 'compromise' does not remove the draw of Anglicanism, I still think the elusive ideal of it is better (at least it reads and sounds better to me, by the Prayer Book) than what I'm not able to find out of Eastern Orthodoxy or Roman Catholicism (the two other options where I live. Though the Continuing church I would go to is actually in Portland, OR, not Eugene where I live.)
Sorry for the longwindedness. Did I convey the draw at all?