Reaves (Safeguarding the Stranger, 195) states that 'most' scholars agree the two passages are similar, with Judges 19 dependent on Genesis 19.
Lasine ('Guest and Host in Judges 19', JSOT 29, 38) suggests that the parallels in the text set up the reader to notice the contrasts, namely that the host and guest in the Judges story act opposite to their parallels in the Genesis story.
Hamilton (The Book of Genesis, Chapters 18-50, 38) says the present arrangement of the historical narrative from Genesis through Judges is meant to show that 'the sins of the nations became the sin of the chosen nation'; Israel became as bad as the nations they were mandated to rise above.
Bringing these sorts of observations together, Brettler (The Book of Judges, 88) posits that Judges 19.29 and 20.1 'allude to Saul's battle against Nahash the Ammonite in 1 Sam 11:7'.
The place names and tribal affiliation in this final episode of Judges are closely connected to Saul. Saul is from Gibeah (1 Sam 10:26), and is a Benjaminite (1 Sam 9:1).
Brettler goes on to list several other parallels between Saul's personal story and the episode in Judges 19-21. Working from these points, he asserts (91) that the story in Judges 19 was largely borrowed from the Genesis version and reworked into a political commentary on Israel's social condition before having a king, with the specific details of the city and tribe involved turning the story into anti-Saul polemic:
A woman is dismembered in a text to express the collapse of pre-monarchical society (Nidicth 1982; Lasine 1984), and more significantly, the inability of Saul to correct that collapse. When read fully, following its genre clues, the text really says: "In those days there was no king in Israel (17:6; 18:1; 19:1; 21:25) and Saul wouldn't be much better, either."