The main difference isn't really who but how much money. One uses a lot of goods and services in ordinary life. Generally speaking one hopes that the provider of these goods and services uses their resources efficiently to provide them for a reasonable price including reasonable profit.
When a leveraged buyout happens (this is true for most leveraged buyouts) a large cost is put into the business that wasn't there before. And this cost does nothing to help make the good or service better. It merely exists so that person B may own the business instead of person A.
So what is the difference between Musk and the previous shareholders? The main difference is that Musk put an enormous cost on the business which will be borne by twitters users and advertisers, and that cost brings twitter nothing more than having musk as an owner.
By himself musk may be no better or worse than the previous shareholders. But just for him to rule over twitter is going to cost twitter a lot of money that will probably reduce the quality of the service.
This is true of most leveraged buyouts and whenever a leveraged buyout happens to a company you use, it is always a good idea to look for alternatives. The official response of the leveraged buyout industry is that the new management is just so much better that it is worth to saddle the company with all this debt and all these costs to just change the management. And the customer will benefit from the better management.
It is yet to be seen whether Musk is such a great manager that he can run a social media company so much better than everybody else to make it worth taking the enormous debt, and do that without having any experience running a social media company and while running two (oh wait - three ) other companies simultaneously.
But generally speaking this is not the case. It might have been the case during the beginning of the LBO industry when there was some truly entrenched bad management in some US companies but not anymore. It is possible to change management of a publicly traded company without doing an LBO, and nowadays stockholders tend to be good about holding their managers to high standards.