Which is correct in using "consider as" of Cambridge and Oxford dictionary?

Simply, these two authorities disagree on this particular point. This problem is a recurring one in the study of all languages and it stems from the fact that given the great complexity and unsettled nature of such a system as a language, not all humans speaking a given language as their mother tongue can perceive it in the same way, and this is true in particular for the specialists of the language. This is one of a reason why there exists several dictionaries. Most of the time the different authorities agree amongst themselves and there are only slight differences such as wording and choice of synonyms. However, sometimes there is a clash, as in the present case.

In this particular case of disagreement, there is no difference in interpretation. As I understand these forms, the choice made by the Cambridge team shows a better style, the reason for that being in my opinion the fact that "as" is a somewhat overworked grammatical word; so I'd rather read "considered to be" rather than "considered as". However, there does not appear to exist a hard and fast argument against using "as", no clear cut logical inference to lead to a categorical prescription.

There might be a more or less great part of subjectivity involved in this usage. Considering "to view as", which is recorded in OALD but not mentioned in the Cambridge dictionary, it can be seen from this ngram that there is a sure inkling that "viewed to be" would not convey the concept as convincingly in the mind of the native speaker.

People sometimes may use "consider as" to mean "consider to be," but if that is the actual intended meaning, it's a mistake because the words themselves don't mean "consider to be" but actually mean the exact opposite.

"Consider as" actually means "consider like." When something is "like" something else, it is not that something else but is merely in some way similar to it. So, if you say, for example, "I consider you as a friend," maybe you mean to call me a friend, but you're actually calling me something similar to a friend, meaning I am NOT a friend. I am merely as a friend, like a friend, similar to a friend, thus not a friend.

"Consider as" is fine phrasing if what you mean is "consider like" or "consider similar to," and maybe you do! The use of "consider as" over "consider to be" in situations can be a Freudian slip, meaning that one is betraying that one either consciously or unconsciously doesn't actually consider that something to be that something else, or to borrow on the above example, you don't actually consider me to be "a friend" and your use of "as" is a conscious or unconscious way for you to avoid calling me "a friend" when the situation seems to be pushing you towards you calling me "a friend."

Therefore, if you mean "consider to be," you should say "consider to be" (e.g., I consider you to be a friend.) or even just "consider" (e.g., I consider you a friend.), but NOT "consider as." On the other hand, if you don't mean "consider to be" but mean "consider as," as in "consider like" or "consider similar to," then "consider as" (e.g., I consider you as a friend.) is a perfectly fine and grammatical way of expressing that.