There are 11 variants at Bodleian Library Broadside Ballads. Since reproducing them here would be mostly redundant as well as very tedious, I will summarize the variations:
NONE of these have a spoken narrative. 1-4: "From the church unto the..." 1-4: "From the churching to the..." 1-5 and 5-5: "...old Father Gripes" 1-6: "daddy" rather than "dadda" 1-7: "While all the way to church, the pipes..." 1-8: "Struck up a lilt..." 1-8: "Play'd up the lilt..." 2-3: "And Muirlips Megs, and Scurlips Scegs" 2-4: "...Dicky Durfey..." 2-5: "And then the girls dress'd out in swipes" 2-5: "And then the girls dress'd out in white" 2-5: "And then the girls dress'd out in whites" 2-5: "And then the girls drest in their stripes" 2-6: "Led on by Tad O'Reilly O, 2-7: "All jigging as the merry pipes" 3-1: "When Pat was asked if his love would last" 3-1: "When Pat was asked would his love last" 3-3: "Arrah! Faith, cries Pat" 3-5: "...her hand he grips" 3-7: "While all in tune the merry pipes" 4-2: "With spirits so gay and frisky, O" 4-3: "...a scroggan or more" 4-3: "...a skirrages or more" 4-3: "...A skirraik or more" 4-4: "...bladder of whiskey O" 4-5: "To the bride's dear health, round went the swipes" 4-6: "That her joy might be nightly & daily O" 4-7: "And as they guttled, the merry pipes" 4-7: "And still has he guzzled, the merry pipes" 5-2: "To see them all footing and..." 5-3: "An opera or ball was..." 6-1: "And now the knot so tipsey had got" 6-1: "And now the lot so tipsy are got" 6-4: "For the throwing of the stocking, O" 6-5: "And round to be sure did not go the swipes" 6-6: "At the bride's expence so freely, O" CHORUS: "Didderum hi, &c." CHORUS: (none)
Dang! I thought making a detailed comparison of all the versions would be an interesting project, but I got sick of it long before being finished. The above list is incomplete, but I hope someone will find it enlightening.