Which, if any, characteristics of bacterial gene transfer is/are useful in analyzing eukaryotic gene ...

Lateral gene transfer is the process by which genes are transferred between species, as opposed to vertical gene transfer in which genes are inherited from ancestors. This phenomenon is common in prokaryotes, and can occur by conjugation, transformation, or transduction. There is evidence of natural lateral gene transfer in eukaryotes, but it is far more relevant in terms of artificial gene transfer and genetic engineering. Genes from one organism can be successfully expressed in a different organism; for example, expression of GFP, luciferase, and various reporter genes. If you want to introduce a gene of interest into a eukaryotic cell, you will most often use transformation. Cells are incubated with the DNA of interest, and then subjected to artificial selection to select for cells that have taken up the DNA from the environment. This same process occurs naturally in bacteria and in single-celled eukaryotes, but can be a valuable asset for genetic engineering.
More recently, specially engineered viruses have also been used to introduce DNA into a eukaryotic cell as a strategy for creating transgenic cell lines or for gene therapy. This process is similar to the mechanism by which bacteriophages transfer DNA between bacteria through the process of transduction.
Thus, studying the mechanisms of lateral gene transfer is both helpful and relevant to understanding the processes by which eukaryotes acquire new genes naturally or through intentional genetic engineering.