Lisa A
Stay on your H4. You are perfectly free to study on an H4.
Your husband's company will have wasted a lot of money getting you the H4 if you abandon it.
Plus your F1 is conditional on being in good standing at your university. If you have to drop out for some reason, you go home. Leaving your husband behind, if that is what he chooses.
Your H4 is conditional upon your marriage. If you study, don't study, whatever, you can stay as long as your husband stays.
?
You don't really cite your "current situation". If you're about to age out of your H4 you'd probably want to look at an F1. If the person you're a dependent to is nearing the end of their visa the same might apply. However if you need to work while studying you could more easily do that on your H4 if you can get an EAD. I'd speak to a lawyer.