Outside of tax deduction differences and discharge rules mentioned in the other answers, one major difference is that the student loans are "term loans" whereas the HELOC is a "line of credit". With a line of credit you have more flexibility because every month you can over-pay and then pull more money back out if you need it. This way your average balance is perpetually slightly lower and you save a little bit of interest.
Another major advantage of the HELOC is that as you pay it down, you have more money available for a rainy day. It could theoretically act as your emergency fund which might free up savings for additional investments.
One disadvantage of the HELOC might be an annual fee (obviously this depends on your bank). Student loans typically don't have any recurring annual fees.