Welcome to the 'Buzz', Kelly.
Here's my opinion:
A split tail has a bitter end with a stopper knot to prevent unravelling of the hitch. This, only one side, or leg, of the hitch is bearing the load. In a traditional doubled rope system, this would be 1/2 the climber's weight...With an eye to eye hitch cord (modern slack tending pulley system [self tailing, etc...]), both eyes terminate to a connector, thus each leg will support 1/4 the climber's weight.
The termination of both eyes allows for a much wider variety of hitch configurations. There's also a seemingly limitless number of hitch cord material/diameter/construction options. Many of these materials are able to withstand much more heat than a traditional split tail cord, giving the eye to eye hitch much more potential for longevity.
Using an eye to eye system allows the hitch to be positioned much closer to the bridge of the climber's saddle, facilitating tending of the hitch during lower rope angle limb walks, etc...this also carries over into vertical ascent situations in that the hitch does not limit how far the climber can reach on the working side of the line during upwards pulls. A proper hitch/climbline combination will make slack tending an absolute dream.
Modern hitch cord will allow easier progression into the popular SRT work positioning climbing systems.
Modern hitch cord can also make you more popular, and more fun at parties, unless it's a costume party and you want to dress up as a throwback. In that case, a split tail would be awesome.
By the way, I have seen some modern hitch cordage sold in split tail fashion, that is one eye and a bitter end. I think this could allow a higher performance cord to be used in a split tail mode. I have no experience with this. I used a closed system until moving into a Hitch Climber system.