First, the spelling of the mantra in Devanagari ("Sanskrit") and Tibetan scripts:
Transliteration: oṃ āḥ hūṃ vajra-guru padma-siddhi hūṃ
Transliteration: oṃ āḥ hūṃ badzra-guru padma-siddhi hūṃ
The following two characters differ (Tibetan script followed by IPA): བ = /ba/, ཛ = /dza/. Why is that? There's no व "va" in the native Tibetan alphabet, so the options are ཝ "wa" or བ "ba". In this case, "ba" has been chosen. Letter ཛ /dza/, instead of the native "ja" ཇ /dʒa/, is commonly used to transliterate the Devanagari ज "ja", being phonetically closer (although not identical). The spelling of "padma" is identical, however in Tibetan the pronunciation becomes "pema". Likewise "badzra" becomes "benza", non-native Sanskrit conjuncts like "dzr" often morph like that. The literal spelling "pema" has also entered some Tibetan texts, though I haven't seen it used for this particular transliteration.
There are also variations (regional/lineage/historical) of the actual pronunciation in Tibetan, so the answer to your question, "which version is more authentic", depends largely on "according to whom". Undoubtedly each Tibetan lineage will hold that their version is the preferred one. If you should find an Indian Vajrayana practitioner from a native lineage, they would probably prefer the Sanskritic version. If you happened to find a heir to the Mahasiddhas of early medieval Bengal, chances are they'd prefer you muttering "bojro-guru podmo-siddhi" instead. To each their own, I say, and all success.
"Is it up to the individual?" Again, it depends. If you follow a traditional Lama who has inherited a certain version, then that's probably what you are expected to emulate. (Be aware that Roman transliterations in Tibetan writings available in English are often approximate, if not crude, and non-standardized. Find a recording and follow that if you want to have it 100% per the source.) If you follow your own lead, then yes, surely it is up to you, and your experience, which variant you may prefer.
If you're a lonely rider on the path to nowhere, you will want to burrow into the effects of each version and try to pin down the mind-space and energy impact conjured by each variant, along with the syllables when individually uttered. (This is worthy practice with any mantra and in any case.)
The greatest benefit follows from no particular pronunciation, but from the skill of entering the mantra and deploying it as a medium for entering the "lotus-born diamond-master" space of awareness, flanked by the energies of the seed-syllables — and in due course embodying all that yourself.