There may be a price differential in the values since you mentioned that your neighbor has a larger home. Of course, the appraisers will take certain factors into consideration: such as style of home, square footage, lot size, updates, etc. Your lawyer can then review the report and make suggestions as to how to proceed.
Then discuss all the relevant details. Is there money changing hands? Who pays what closing costs? Are inspections needed? Mortgage considerations? What date do you want to do this? What fixtures and appliances are being left and which are being taken? Things such as this.
Now, get an attorney involved and let him do the rest of it.