I think you'll find that it is essentially the same. In both cases you are unable to fulfil your contractual obligations and the mortgagor is left with the expense of selling the house and recouping any difference from the mortgagee. So it is likely that the bank or building society would class them as the same and you would suffer the same loss of status in the long run.
You could try to negotiate a settlement with the bank or building society in which you either take a mortgage holiday and lengthen the timescale of the mortgage, or you could agree to pay only the interest for a set number of years, or you could enquire about selling your house to a company who will let it back to you for a rent which is lower than your present mortgate repayments. However, it would be remiss of me not to point out that there are more cowboys in that field than in almost any other and unless you get some really good advice you could be jumping from the frying pan into the fire.
Good luck with whatever you decide to do.