The contrast between a liberal arts college and an Ivy League university is significantly less pronounced than a comparison between a liberal arts college and a state university. However, in writing a persuasive essay favorably comparing a liberal arts college against an Ivy League university, there are several arguments you might find helpful.
First, the admissions rigor of liberal arts colleges offers significantly more flexibility than the member schools of the Ivy League. All of the latter have, generally, similarly intense expectations of applicants and correspondingly low rates of acceptance. Liberal arts colleges, however, run the gamut from the very competitive (such as Amherst College) to the less competitive (such as Augustana College).
Second, liberal arts colleges—by definition—only offer baccalaureate degrees. As a result, they tend to be highly focused on the education of their undergraduate students. In contrast, Ivy League universities offer degrees up to the doctoral level and must balance instructional obligations against the university's research and other needs.
Third, some liberal arts colleges offer unique curricula that aren't replicated at any of the eight Ivy League universities. For example, Thomas Aquinas College is known for its "great books program" in which all students pursue the same course of study based on the great books of Western civilization. Deep Springs College has a unique campus life in which students and faculty participate in tending to a working ranch.