Bridge Financing?

Hoping I can get some clarity/opinions on this situation:

Planning on buying a condo first, then selling my house (which I'm confident will sell quickly in this market).

Assuming the price I buy at and sell at are approximately the same. No mortgages involved. Hoping to coordinate dates so I don't need any bridge financing, but if I can't pull that off and need to bridge a few days or weeks between closing, I've been looking into bridge financing options.

Spoken to two different banks that I deal with and each gave a different option:

Bank A - they said its not a bridge loan, but they would be putting a mortgage on current property to draw equity out, need appraisal of current home, they advance the amount on new home and loan is paid out when sold

Bank B - they would put a line of credit on the new condo and bridge anything extra on the old house, paid off upon sale

So basically I'm wondering is one of these preferable over the other? Obviously both have interest and fees associated with them which seem to be roughly equal, wondering if there are other things I should be thinking about or asking or looking out for??

Thanks in advance!