Is either of these two sentences correct? If both are correct, is one of them more common than the other?
[some arguments...] Hence the need to make an educted guess.
[some arguments...] Hence the need for an educated guess.
Both are correct. Subjectively, the need for is more idiomatic, and shorter, and Google Ngram Viewer shows that it is factually more popular (although the gap is closing).
Your comparison between to make X and for X is not quite correct.
What is really being compared here are two slightly different meanings, but your phrasing is making it look like a question of language.
The form need for an educated guess states what is needed - the noun-phrase educated guess.
The form need to make an educated guess states what one needs to do to get it, the verb make.
The difference is not one of one being better English than the other.
The latter gives more information. This can therefore be better, but it can also be quite incorrect. If the arrival of guests means that I need a cake, do I need to make that cake? I might, if my baking was often-praised by the guests in question, or the social group I was in highly favoured home baking. I might need to buy a cake if my baking was poor or I was in a social group in which store-bought was considered a more extravagant treat (not common these days, but certainly the case in the past). It might be of no consequence whether I bought it or made it myself.
If I'm arriving at an airport and will need to make a journey covering several different destinations over a short trip, then what I need is a car, but I most certainly don't need to make it! Here then, I've a choice between need for a car and need to hire a car. Again, the latter provides more information, so whether we favour it or not depends mostly on whether we want to explicitly give that extra information or not.
As Jon Hanna says, it's misleading to frame this as a choice between need "to make X" and "for X".
For most contexts, both versions mean exactly the same. But the "make" version strongly implies the "educated guess" (which obviously hasn't yet been "made") must be made by either the speaker or audience, or someone acting directly on their behalf.
The other version could be used in situations where one or more "educated guesses" have already been made by others, and the need is simply to locate one, not make it (phone an expert, maybe?).
Apart from that distinction, it's just a stylistic choice. But taking a closely-related construction that occurs often enough to track, idiomatically people tend to speak of the need to [do something], rather than for [doing it]. From Google Books...