Many critics of Christianity often take the 'resemblance' of Christianity to various pagan myths to be evidence that Christianity itself is merely a variation of these myths, though perhaps mapped onto actual history. With that last qualification begrudgingly conceded to due to the wealth of available historical evidence corroborating Christian claims. Though, this very fact of historicity undermines the claims of similarity immediately, at one level, because pagan myths lack this element almost entirely.
Still, these critiques do present some questions that Christians have to confront: Is there such a resemblance? If so is it a significant resemblance, or merely a superficial one? If there is some substantial resemblance on some level, what does that mean? Does it mean that Christian claims are untrue, or that scripture is merely a re-tooled pagan myth?
Without even being particularly well-versed in history and simply utilizing formal logic, it can easily be seen that, even if there were substantial pagan precedents to Christianity, it wouldn't say anything about Christian truth claims, nor necessitate the conclusion that Christianity is also fully -- or largely -- myth, even if it had -- in some sense -- been preceded by religious practices and devotions in late antiquity. And, once you actually do delve into the details of history, this becomes all the more obvious because many of the supposed similarities to Christian belief and thought are superficial or non-existent, while the similarities that do exist are easily explicable within the bounds of Christian thought.
A podcast I listen to regularly (Take the Stand) recently tackled this issue, and they do a good job of employing the traditional (and potent) Christian apologetics on the issue. Some supposed similarities are simply fabricated; others are exaggerated; others exist but are superficial; others are legitimate similarities but only analogous to a single aspect of Christian belief (if that), not to the whole; Pagan myths differ in their very intent and content, whatever details may be vaguely similar.
On top of this, Christian thought maintains that Christ is the creator of all things and that Creation expresses the work of the creator in its fabric. With this being the case, its even less surprising that humans -- even prior to the Incarnation -- should stumble upon this truth, though necessarily in a pale, shadowy, incomplete form.
After I had just listened to this episode, David Bentley Hart wrote a new article on this matter as well. Hart takes a much different approach, instead choosing to acknowledge significant pagan analogs to Christianity "in the intensity of piety, in the spiritual longings it answered, even in its liturgical and sacramental conventions." Part of the intent of Hart's piece seems to jolt Christians out of their reactionary denials of any similarity, instead noting that certain stylistic and spiritual similarities are undeniable, and that this fact should hardly be surprising (though Hart deliberately narrows his focus to the styles of religious devotion, rather than the areas of moral or narrative content, historicity, truth, etc.)
Christianity is, in fact, historically rooted, so there's no reason to suspect that its worship, devotions, or language would differ markedly from the prevalent styles of the time. What we as Christians need to maintain is not complete originality on all matters, though we must argue in favor of the historicity of Christ, and deny claims of 'legend' or 'myth' being significantly present in scripture. What makes Christianity important and different is that it is true, not that it is wholly original in its human devotions or stylistic conventions.
Christian thought does make significant claims to telling a new narrative of reality and being and professes a content that is unlike any other in the ultimacy and finality of its truth (pagan myths were not even believed to encompass a complete account of being, but rather were almost always accounts of gods within an economy of gods) and on this count we should persist and be vigilant. The actual content of the Christian faith is something entirely new and original and true, and none of the vague, imprecise approximations of that content that existed in late antiquity (some of those being influenced by Christian thought, and not the other way around) do anything to circumvent this claim. Nor do they make the conclusion that the authors of Biblical texts 'copied' or 'appropriated' significantly from pagan myths any less untenable.