Zinc sulfate is a mineral salt that reacts with water to form a strong acid (sulfuric acid) and the compound zinc oxide, which is practically insoluble in water. By comparison, zinc gluconate is a weak organic salt that dissolves to form positively charged zinc ions and negatively charged gluconate, which is a natural, non-toxic compound found in all human tissues.
Its important to check how much 'elemental zinc' is in each product, that is what counts.
Taken internally there is not a lot of difference between the two.