[wynn]

The structure on the left hand side has the positive charge on a tertiary carbon. Normally, I will pick that one as the molecule with more stability; however, although the structure on the right hand side has a positive charge on the oxygen, the oxygen also has an octet. So, which of them is more stable???

[Sophia7X]

Generally the more stable structure has the less electronegative elements with a positive formal charge, but I think the right structure is better and more significant than the left structure because BOTH the carbon and the oxygen have an octet, while the carbon in the first structure lacks an octet.

[Babcock_Hall]

One might rephrase your question as "Which of the two resonance forms makes the greater contribution to the true structure?"  I lean toward the one which gives all atoms a full octet, but perhaps a physical organic chemist should have the last word.