Importance of undergraduate honors thesis vs. research published in undergraduate research journal, for graduate schools in the United States?

I have the option of graduating from my university (U.S.) a semester early. If I do so, I would not be able to complete my honors thesis and have it approved by the honors committee of my university. However, I would still complete the same research project, write up the manuscript, and probably submit it to my university's undergraduate research journal.

For admission to psychology PhD programs in the United States, how important is the actual "honors thesis" component?