With product options you will create a new product for each option, with its own inventory management. When you use custom fields, you have one single product linked to the inventory. You can create several options for the product in question, but no separate products.
Let's say you have four sizes (S, M, L en XL) of a given single product. When you use product options, a separate inventory is made for each size. If a customer buys a product in size S, it will be deducted from the size S stock. Every size constitutes a separate product.
When you use extra fields, you have one single product with a single inventory. It doesn't matter whether a customer buys a product in size S or XL, they will both be deducted from the same inventory.
Product options will be listed in a drop-down menu. If you want them presented in another manner, you can only do so when you use custom fields, such as text fields, check boxes and radio buttons.