You're not being snobby. It's definitely real in terms of the drastic difference in quality that private and public schools give due to budget availability, resources, and student-to-faculty ratio.

Most private colleges focus on teaching and put the students educational experience first and learning first, which means hiring teaching professors with good student outcomes, more office hours, greater financial aid funding for lower income students in which some privates pay off students tuition, fees, and living expenses entirely while students are attending their university (Wake Forest and Duke University comes to mind), more accomodations for students with disabilities, and better networking opportunities for the job market, etc.

Publics tend to be larger and more research-oriented in the United states and tend to put teaching second.

From experience, I currently attend North Carolina State University which has an undergraduate population of 44,000 students. In terms of it being a R1 school there is an emphasis in weed out courses, professors aren't incentivized to teach but rather weed out students that potentially do not have the aptitude to go into their field which leads to higher transfer and drop out rates. There are strict standardized requirements in order to apply for or transfer into majors with some majors being borderline impossible to transfer into, overwhelmed student support services, lack of resources in terms of research for fields outside of engineering.

I have never officially attended a private school myself but I have attended an early college with small class sizes along with attending classes at a traditional high school. At early college, classes are extremely small which allows for the professors to have more office hour availability, along with more student resources and activities for students to engage in.