Fairly strong. There are DoD and DoE requirements that bias in favor of pushing R&D funding into Public Universities.
GATech's early lead in computing was because of it's longstanding relationship with the US Navy's Nuclear and Aerospace Programs (both of which have significant HPC needs).
It's a similar story at UCB, UIUC, UMich, UT Austin, UW, etc.
Aside from MIT, Stanford, and Cornell, the bulk of DoE and DoD funding ends up at public universities.
> private schools end up a better place to study CS due to their smaller class sizes and less variance
I attended an Ivy Level CS program for undergrad. My sibling attended a Tier 1 public school program for CS.
My sibling's CS education was superior, as the public university was able to hire way more faculty at better rates, as most decent public universities have multiple DoD and DoE universities and grantmakers to entice faculty and graduate students.
If it isn't Stanford, Cornell, or MIT, I'd say the CS curriculum is middling at a private.
I myself wish I attended GATech instead of my supposedly "prestigious" undergrad as the research and industrial opportunities at a Tier 1/2 Public CS program like a upper Tier UC, UW, GT, UIUC, etc are hard to beat almost anywhere.
I think the main benefit an elite private school might have is a better support system, but by and large, the student base is largely comparable - if you're Berkeley EECS or UT Austin/UW direct CS you would have had stats comparable to a Stanford or MIT undergrad