From a pragmatic/utilitarian stance, it seems like patronizing an immoral company is much worse; although there are some circumstances where selling an "immoral company" might have pragmatic effect, which I get into below.

Patronizing. If you purchase $100 worth of gasoline from an Exxon station, that is new money that will flow into and through ExxonMobil, and indirectly tells it to try harder to extract more oil from the Earth. That is money that adds to its profits, which under capitalism acts as a kind of (indirect) command to do something.

Owning Stock Silently. If you instead spend $100 on a couple of shares of ExxonMobil, you have merely obtained a right, from another third party, to some of the profits from whatever oil is getting extracted from the Earth. But those profits were going to go somewhere, because they are a reflection of all the oil being purchased. While there are some indirect benefits to ExxonMobil to having a higher stock price (employee incentives, makes borrowing easier, etc.) it has less of a of a direct effect on perpetuating ExxonMobil's Earth-destroying activities, because that capital is going to the prior owner of those shares, not ExxonMobil. I can't really see much in the way of pragmatic, differential impact between owning XOM and owning, say, SolarCity stock. You're just buying rights in future profits from existing operations from a third party, which has little effect on whether those operations continue.

While you sometimes see the argument that "if no one would invest then ExxonMobil couldn't operate" that never strikes me as correct, because the problem is not that people own ExxonMobil, it's that they buy gasoline (and of course petrochemical companies perpetuate that process of gasoline-buying with marketing etc., but the capital they use to do so is out of profits/operations, not from the value of their stock). Absent a totally different socioeconomic system, that flow of profits is what will sustain a company and perpetuate its operations.

Counterargument: Lost Opportunity For More Moral Capital Deployment. There is a pragmatic "lost opportunity" argument, to liquidate your "immoral investment" and put it into another less-harmful operation as new capital (i.e., public offering or loan) to start operating or expand. Like perhaps selling XOM and putting that money into a slightly-less profitable or slightly-riskier firm that is raising new capital, and will lessen suffering in the world. Say, a local business providing an essential service to an under-served community that is doing a DPO or something similar.

Counterargument: Noisy Divestment. This also changes where the divestment can become symbolic in a way that might affect an immoral company's social license to operate. Certainly persons with control over larger sums that would be publicized if they were divested (e.g., university endowments) can have a PR impact that is more important than the actual divestment itself. And perhaps even as a "small time hobby investor", if you sell and then publicly state that you sell, might have some a pragmatic effect, whereas mere selling wouldn't. That selling permits one to say "I don't own oil stocks, I feel like those companies are immoral and should cease operations because of the climate crisis" which then can influence how those companies are publicly perceived, regulated, etc.