Learn Turkish: Eski sürümün aksine, bu cihaz oldukça hızlı. - Unlike the old version, this device is quite fast.

The word aksine (unlike / contrary to) requires the specific noun or pronoun before it to be in the genitive case. You can think of it as forming a possessive phrase: literally "to the contrary of the old version." Therefore, sürüm (version) takes the genitive suffix -ün to become sürümün.

Is there a difference between using aksine and tersine here?

No, in this context, they are completely interchangeable. You could just as easily say Eski sürümün tersine and the meaning ("Unlike the old version") would remain exactly the same.

oldukça usually means "as it becomes" or "the more it is" (from olmak + -dıkça). Why does it mean "quite" here?

You're right about its grammatical roots! While the -dıkça suffix usually means "as long as" or "the more," the specific word oldukça has evolved into a fixed adverb of degree. When placed before an adjective like hızlı (fast), it is no longer a verb form and simply means "quite," "fairly," or "rather."

Would it be wrong to add the "to be" suffix -dır and say oldukça hızlıdır?

It wouldn't be wrong, but it changes the tone. Omitting -dır is standard for everyday spoken or casually written Turkish. Adding it (hızlıdır) makes the sentence sound more formal or authoritative, like a line from an official tech manual or a professional written review.