Why did some civilizations develop a logographic writing system as compared to an alphabetic one? What causes these discrepancies?

Before answering your question, there are several things that should be pointed out.

First, the opposite of 'logographic' is not 'alphabetic' but 'phonographic'. There are phonographic scripts that are not alphabetic. Japanese kana is an example; every kana glyph more or less represents a syllable.

Second, there are no writing systems that are purely phonographic or logographic. (See Ideogram: Chinese Characters and the Myth of Disembodied Meaning by James Unger) A purely phonographic writing system would be something like narrow IPA transcription with no punctuation and no spaces between words. On the other hand, a purely logographic writing system would resemble something like a code book, where every word would have its own symbol and there would be no pronunciation clues in the symbol. Both of these systems would be far too onerous for everyday use.

In reality all writing systems are clustered somewhere in the middle of a scale between purely phonographic and purely logographic. Toward the phonographic end of the cluster are more "phonetic" alphabets like the Spanish alphabet, in which every letter more or less stands for a phoneme in spoken Spanish. But even the Spanish writing system has logographic elements like using spaces to divide words and capital letters for proper nouns.

On the logographic end of the cluster is Chinese characters. However, even Chinese characters have phonographic characteristics. First, with very few exceptions, every character represents exactly one syllable. In addition, approximately 80% of all Chinese characters are a combination of a semantic element and a phonetic element that, respectively, give a hint as to the meaning and pronunciation of the word the character is used to write. (See Chinese Language: Fact and Fantasy by John DeFrancis) Finally, as spelling becomes increasingly divorced from pronunciation in languages like English and French, those writing systems move toward Chinese at the logographic end of the cluster.

Now that that's out of the way, back to your question. First, all writing systems started out as incomplete pictographic writing systems. Pictographic writing systems are 'incomplete' because cannot be used to write ~~any~~every possible sentence or phrase in the language. The writing systems then become complete when their users discover the rebus principle, i.e. they realize that they can use the pictographs to represent only pronunciations rather than just the original referent depicted by the pictograph. To my knowledge, this discovery was only made three (correction: or more likely four) times independently in human history: (edit: once) in Central America, (edit: twice) in the Middle East, and (edit: once) in China. By using the rebus principle, the pictographic writing system ceases to be pictographic, and instead becomes a phonographic syllabic writing system. From there alphabetic and other phonographic writing systems developed. (I am going to stop here about development of writing systems in the West, Middle East, and India because it's out of my specialization. If anyone could fill in the details or correct me where I am mistaken, that would be greatly appreciated.)

However, in the Chinese writing system, the rebus principle was not the only one at play. There also appears to have been a principle that different words or morphemes should be written with different glyphs. A good example of this is character 來, which originated as a pictograph for barley (now pronounced 'mai4'), but came to be used for the word meaning 'come' (now pronounced 'lai2') which was originally pronounced the same. The word for barley then came to be written with 麥 instead of just using the same character. Other principles were used to develop more characters (detailed in Chinese Language: Fact and Fantasy by John DeFrancis), namely doubling or tripling the original character (e.g. 木 -> word for wood/tree; 森/林 -> words for forest), or combining a sematic element with a phonetic element (e.g. semantic element 米 'rice' + phonetic element 唐 tang2 'Tang (dynasty)' -> 糖 tang2 'sugar').

TL;DR Complete application of the rebus principle allowed the development of phonographic writing systems. Incomplete application of the rebus principle with formulas for developing more characters led to tens of thousands of Chinese characters where generally one character represents one morpheme.