It's actually neither.
You can use the acronym FANBOYS to recall the seven coordinating conjunctions (for, and, nor, but, or, yet, so).
A subordinating conjunction has to introduce a subordinate clause, which as well as cannot do. Common subordinating conjunctions are although, as, even though, etc. The reason as well as cannot introduce a subordinate clause is because what follows cannot have a subject and verb, which are required in any clause, whether subordinate or independent. For instance in the sentence
As well as swimming, Linda enjoyed cycling.
it may look like you have a subordinate clause because the introduction to the sentence is followed by a comma, but swimming is a gerund (a noun formed by a verb), and there is no subject before the comma, so as well as introduces a phrase, not a subordinate clause.
As well as is a conjunction, though, and is sometimes called a "phrasal connective." Other examples of phrasal connectives are in addition to and together with.
The conventional grammar rule is that as well as does not mean the same as and because it does not create a compound subject (a subject made of two or more nouns). For instance, see the two examples below and see that the verb changes from plural to singular with the change of conjunction:
The soloist and the rest of the string section were very talented.
The soloist as well as the rest of the string section was very talented.
Above, as well as introduces a parenthetical phrase that can actually be set off by commas:
The soloist, as well as the rest of the string section, was very talented.
For that reason, the verb is singular because the soloist is a simple subject and is singular. Hence, as well as does not serve the same purpose as and in terms of connecting clauses and subjects.
Note: It can, however, serve the same purpose as and in more simple cases. Flip my first example sentence around and you'll see this: "Linda enjoys cycling as well as swimming." This has no difference in meaning to "Linda enjoys cycling and swimming," though the second construction is clearer and more common.