Interesting matchup.
Haley has been rather unpopular in South Carolina, which suggests she's a weaker candidate, although it's also possible that some of it stems from bigotry and a toxic political culture. She may play better on a national stage.
Booker would get a lot of younger voters, and he would presumably keep high margins of African-American voters, although Haley would be more of a milestone.
I suspect Booker's a better candidate, but this would likely be a Republican leaning cycle.
As for running mates, Nelson's old but he could be Booker's Biden, with the added bonus of making a very important state more favorable. Becerra could help with Hispanic turnout. Tulsi Gabbard would be a disaster, due to her lack of experience and religion. Elizabeth Warren is another Northeastern liberal, so she seems like a poor fit. If Landrieu can win reelection, she would be a strong fit, with a combination of experience and appeal to female voters.
Jon Kyl would be Haley's Biden, but he may be too old and divisive. Paul Ryan handled himself well as a national candidate, and can help in the midwest. Portman has similar strengths. He isn't as charismatic, but that's less important for a Haley than it is for a Romney. Sandoval is Pro-Choice, so that could alienate certain voters. Mike Lee may not be a team player, although a young conservative legislator isn't a bad choice for the ticket.
It it's Booker/ Landieu VS Haley/ Lee, I could sort the states in the following categories...
Safe Democratic...
California, Delaware, DC, Connecticut, Hawaii, Maryland, Massachusetts, New Jersey, New York, Rhode Island, Vermont
Likely Democratic...
Illinois, Maine, Oregon, Washington
Leaning Democratic...
Michigan, Minnesota, New Mexico, Nevada,
Toss-Up (Democratic Lean)....
Colorado, Iowa, Nevada, New Hampshire, Pennsylvania, Wisconsin,
Toss-Up (Republican Lean)....
Virginia, Ohio
Leaning Republican....
Florida, North Carolina
Likely Republican...
Arizona, Georgia, Indiana, Mississippi, Missouri, Montana,
Safe Republican....
Alabama, Alaska, Arkansas, Idaho, Kansas, Kentucky, Louisiana, Nebraska, North Dakota, South Dakota, Oklahoma, South Carolina, Tennessee, Texas, Utah, Wyoming, West Virginia
So, the default map would be...
Booker- 272 electoral votes
Haley- 266 electoral votes
If Booker nominates Nelson, he likely becomes the favorite in Florida, which gives him 301 electoral votes to Haley's 237.
Portman makes Ohio safer for Haley, but it's not enough.
Ryan might be Haley's best running mate in terms of swinging a state, as three points in Wisconsin could be a big difference in the outcome of the election.