If I have to claim bankruptcy, is there a difference between having a home equity line of credit or a mortgage on my home?

A home equity loan and a mortage are the same from the point of view of a bankruptcy; both are secured debts which, if you do not reaffirm them, can result you losing the home (though not being liable personally or for any remaining deficiency--the lender can take the home if you do not reaffirm and agree to pay, but can't otherwise sue you; this is a slight oversimplicifation, but will suffice for this purpose).

A home equity line is also treated the same, to the extent money has actually been drawn from it (i.e. to the extent it has been used).