Married filing separately with a home sale

My wife and I are married but separated, living in two different places in Massachusetts.  We sold our home and agreed to split the proceeds of the sale equally.  The proceeds were large.  I am thinking we  need to file using status Married Filing Separately but I don't know if we need to report the proceeds of the sale and if so, will it result in a tax on the sale for either one of us?  Or is there an advantage to filing Jointly?