Up to $2,500 in student loan interest can be deducted from your taxes without itemizing, but the benefits begin phasing out if your MAGI is over $65k/$130k and it is not deductible at all if your MAGI is above $80k/$160k, for 2017 (for single/married filling jointly).
Previously, HELOC interest was deductible like a normal mortgage if you itemized deductions, but it seems the new tax law means HELOC interest is no longer deductible, except under specific circumstances.
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.
Any good financial advisor will recommend against borrowing money against your home unless the borrowing will result in improving the value of your home. If for some reason you fail to pay your HELOC you will end up with a lien against your property, but if fail to pay a college loan for less than 270 days you will only get penalties. Or if the value of housing drops like the bubble burst in 2007, could result in negative equity, making it very difficult or impossible to sell without paying out of pocket or doing a short sale.
Most HELOC loans are variable interest rates.
Take a look at college loan refinancing options like: