The first version features the Dubliners and the Pogues, and the second version is by the Dropkick Murphys. When the guy with the long gray beard sings in the first version, that's the singer from the Dubliners. You're hearing a straight-up traditional “Irish pub song” rendition of the song. Note how the lyrics can clearly and easily be heard- this is a defining feature of real folk and traditional music.
The other singer is the much-revered Shane MacGowan of the Pogues, an early Sex Pistols follower who started his own band to play punk-influenced folk music. The Pogues always performed with the energy and intensity of punk rock, but the instruments used are traditional Irish instruments. Note how the lyrics cannot be heard clearly- that's the punk rock influence. It's raw, it's exciting, and it's fun- but it's not the traditional way to do it.
The second version of the song is by the Dropkick Murphys, a Boston-area punk rock band with deep roots in the Boston hardcore and non-racist skinhead scenes. The Dropkick Murphys are sometimes described as heirs to the Pogues, because their band includes a bagpiper and they sometimes cover old Irish pub songs like this one. Essentially, though, they are a straight-up punk band, and their rendition of the song is very much like a punk song.
Traditional pub song, folk with a hint of punk, and punk with a hint of folk. Three very different interpretations of “The Irish Rover.”