Well I'm an EE so I'm obviously ignorant about research at both schools in regard to ChE, but since ~any~ advice is welcome I would say, based on my EE esperience:
CORNELL ALL THE WAY!
Getting addmission to Cornell Engineering is a huge achievement, and with a full scholarship your question sounds kind of surprising! The issue of minor ranking variation in US news Graduate programs is really quite meaningless.. (If you want to feel better about Cornell, see the national rankings of US news, QS rankings, Shanqhai rankings, and Times.. I'm fairly certain Cornell is way ahead of UT Austin in general. Plus it's an ivy which is extremely prestigious when you're in a cocktail party surounded by people who know nothing about engineering/research. As for research quality I think that depends on the research lab and professor you're going to work with.. This certainly applies to EE labs and professors where you might prefer Austin if you'ld like to work in Signal Processing or Cornell for Robotics.. Afterall they're both excellent research schools)
All the best