We say of these particular Eastern churches “they have a different spirituality, different terminology, different emphasis, but it is the same truth, and it is just as good as what we say and do, and vice versa”. That’s how Protestants view each other (and how they view us as well!).
When I say “Protestants”, I refer only to the denominations that claim this title — Presbyterians, Methodists, Anglicans, Lutherans, Reformed, and so on. Baptists vehemently deny that they are Protestants. I do not normally think of Pentecostals, Holiness, Assembly of God, Church of God (any of them, Cleveland TN, Anderson IN, and so on) as being Protestants either. When I was a child, I occasionally went to the COG (don’t remember which branch), they give powerful witness and I liked it very much. Their Vacation Bible School was amazing.
Some use “Protestant” as a shorthand term for “non-Catholic Christians who are not Eastern Orthodox”. That’s not quite right.
There are groups — the Wisconsin Evangelical Lutheran Synod (WELS) comes immediately to mind — that are convinced they have the most perfect version of Christian truth. For most Protestants I’ve encountered, though, they may be a Lutheran at one point in their lives, a Presbyterian at another point, and so on. It’s really a fairly indifferent issue to them, and has more to do with “how they grew up” or “the way they were raised”. Or they may choose a “compromise church” if they marry someone of another denomination. And of course there is the matter of “this church believes the most like I do” — picking the church that suits you, so to speak, instead of recognizing “the truth” and changing oneself to conform to it.