It is hard to answer this because a lot of the trite answers are indeed false. A computer science student may be more able to tell you whether an algorithm is O(n^3) or O(2^n), but the normal (and experienced) programmer will be able to tell you either is "slow" and fix it just as quickly.

But there is a style of thinking that can come out of a study of computer science that can be very difficult to obtain on your own, and enable you to build larger and better systems than all but the very, very, very best of self-taught programmers, and while it's hard to put that difference into words, it's mostly the study of maintaining invariants in the code from both a theoretical and a practical standpoint. Or, if you prefer, a way of thinking that helps create and enforce a mathematically-strong form of conceptual purity in your code.

Those who don't have this background, and I very much include people who took the courses but just sort of skated through without absorbing anything, will often have problems with any API I create that requires certain constraints, such as being careful at what point they access local information vs. remote information. Their use of the APIs will be sloppy and hacky, because they don't really understand how they work or what they are for. The constraints I am thinking of are purely technical, a particular server/client split, so when I say you can not do X it is not merely me being an academic prick, it is because it is actually impossible to do X because at the time your code runs you are literally in the wrong place. Explaining this fact is easy, but explaining how the system conceptually wraps around this constraint and works the way it does is a challenge.

And APIs designed by such people, while they may get the job done, tend to be very brute force (for lack of a better term) and to lack any sort of firm foundation, such that the moment a requirement even slightly changes we have to make massive (and often hacky) changes to them.

Unfortunately, it is impossible to provide examples in the scope of a single post, because all small examples will not show the issue. It's a larger pattern of issues that tend to start interacting with each other, which is where the real problems emerge.

It is also the case that a proper path chosen through a computer science program will take you through some eminently practical theory that will make you a vastly more powerful programmer, and is very hard to pick up on your own. By far the biggest example of this is compiler theory. If you are currently in college and still have the opportunity to take your local compiler course, take it. I don't write very many "compilers", but I have now written quite a few "interpreters" and it has enabled me to complete projects that could not have been completed any other way. Getting a formal grounding in signal processing is also a good idea, that one can be hard to pick up later and has surprisingly useful intuitions for a lot of high-speed networking tasks. A formal grounding in networking can be good, though a lot of courses unfortunately seem to just march through TCP and the OSI model, which you could relatively easily just read about.

The fastest way to obtain this basic understanding if you are a good programmer but lack the formal education is one of really, honestly working through SICP (and not just reading it), or becoming fluent in idiomatic Haskell, with special concentration any time someone talks about "enforcing invariants via types". (Personally, I believe Haskell has completely supplanted Lisp as "the language to learn to expand your mind even if you have no intention of using it", but be sure you stick with it for a bit. Learning how to string together a couple maps and a fold is not where the interesting stuff is, it's what the interesting stuff is made out of.) Also, break yourself of the subconscious idea that academic === useless. As someone who tends to straddle the border I will completely agree it isn't all useful, but it isn't by any means all useless either.

And just let me reiterate as my closing point that it is absolutely possible to go through even a very good Computer Science program and fail to absorb the useful lessons it has. Presumably these are the people claiming it's "useless". I have to admit I tend to not have a high opinion of people who managed to go through a solid program and come out with nothing. (There are also some complete wastes of programs, so YMMV.)