One simple way to look at the difference between a PREP (preposition) & a CONJ (conjunction) is that while a PREP is a word (or words) that placed before a noun or pronoun to show the kind of relationship the person or thing denoted by it stands in regard to something else, a CONJ is a word (or words) that merely joins together sentences and perhaps words. A PREP not only joins words, it governs a noun or pronoun, which usually is the object of the preposition; a CONJ merely joins and does no other work.
In courageous as well as strong, the phrase ‘as well as’ means ‘and in addition’. It merely joins two adjectives together. It is a CONJ., a coordinating PHRASE CONJ. You may even loosely translate it into ‘courageous and strong’. In The rhetoric [of the Justices], as well as the reasoning, is appreciated" (Benno C. Schmidt, Jr.), the phrase ‘as well as’ means ‘in addition to’. It shows in what relation the noun ‘the reasoning’ denoted by ‘as well as’ stands in regard to ‘The rhetoric’ which happens to be a noun also. So what the sentence means is this: In addition to the reasoning, the rhetoric is appreciated. Reasoning is appreciated, so is rhetoric. ‘Reasoning’ is the object of the PREP ‘as well as’. The difference in meaning might be slight; they do perform very different grammatical function.
We will, as Avangi did, use ‘except’ for another example. In she hardly ever goes out except to visit her mother, “except’ here merely connects 2 parts of the sentence together; it is a CONJ. In She goes out every day except Sunday, ‘except’ not only joins ‘every day’ and ‘Sunday’, it shows what or how in relation the noun ‘Sunday’ denoted by ‘except’ stands in regard to ‘every day’. ‘Except’ in this sentence is therefore a PREP. It governs ‘Sunday’ which is the object of the PREP 'except'.
Some words are used not only as PREP, CONJ but also as an adverb. Take the word ‘since’, for example. In I haven’t slept since yesterday, ‘since’ is PREP. In we’ll go since you want us to, ‘since’ is a CONJ. In I haven’t seen him since, ‘since’ is an adverb.