HI iacdxb,
The first difference is certainly given that the Edge-Cut has an interface (Attribute Manager) and the Connect Point/Edges has not.
The Connect Point/Edges creates just the connections of half the edge to edge or point to point. Sure, in edge mode use the command twice and your get three new edges among the selected, but it is rather a fast and quick way to get a middle edge among them or an edge between two points or among many.
The Edge-Cut itself lets you chose more, even if an N-Gon is preferred, which the Edge-Cut delivers only (if at all) in the end of each new edge “path”.
The Edge-Cut has advanced settings, such as Offset, Scale and Subdivision and optional the before mentioned N-Gon checkbox.
I found it always rude “to state the obvious”, which is certainly not my intention here, but what more can or should I say than what is given—other than in the manual already?
The Connect Point/Edge is a quick but limited way, compared to the Edge-Cut, but the Connect Point/Edge has an option that the Edge-Cut has not: connect points.
The option to have N-Gons is a valid advantage for modeling, not suggested to keep those, but it keeps things clear for the time being.
The Menu sorts it in a command and create sub-menu, perhaps a nice indicator, as I think that create shows more the use for a user/artist input. While the command is kind of fixed and faster.
I hope that helps, there are often several ways to do things, and sometimes it is more important what the artist prefers in a given situation, than an absolute measurement what “is the best” all the time.
All the best
Sassi