These contests clearly were more about getting in necessary Spring Training work and having fun with this brief diversion from Arizona. Even in Cactus League matchups, though, this rivalry has no letdown.
As an example, there were Cubs fans standing for the final out on Friday night, not exactly a prevalent sight throughout these preseason contests. So, imagine, if you will, how this rivalry would play out if it took place in late October, as part of an L Train World Series in Chicago?
Jake Peavy has envisioned part of that scenario. After making his first Cactus League start for the White Sox Friday in Arizona, the South Siders ace said his team has what it takes to win the World Series title if it stays healthy.
It's the same sort of confident Spring Training claim Ryan Dempster made about the Cubs two years ago. And after throwing three scoreless innings in Saturday's victory over the White Sox, Dempster wholeheartedly seconded the bold frame of mind shown by Peavy.
"Every team should think that way," Dempster said. "You should feel that way as an individual and with the team as a whole. Health is the biggest thing. Teams that win usually avoid those things.
"The White Sox have a very good team and a strong pitching staff. They're going to be a tough team. And just like us, I feel like we're going to be a tough team to play against. That's the key, where we're at three weeks from now, making sure we're healthy and ready to go."
Dempster's squad won both of these weekend contests, by 6-5 and 8-7 tallies, avenging last year's two-game sweep by the White Sox in Las Vegas. Of course, it's hard to get a truly accurate reading about either team when so many innings are being played by Minor Leaguers with jersey numbers in the 80s.
But White Sox manager Ozzie Guillen, once again the toast of the Big League Weekend as the one-time Las Vegas Stars shortstop coming home, had a bitingly sardonic explanation for this particular change of fortune. Cubs manager Lou Piniella made the trip to Las Vegas last year, but Alan Trammell ran the show this year.
"Alan Trammell is a way better manager than Lou Piniella. He beat me twice," said Guillen, flashing a mischievous smile, while poking fun at his old friend. "If Lou wants to quit right now, it's a good time to do it. Alan Trammell knows how to handle the game better than he does.
"It shows in the paper tomorrow. He got two wins. They showed they don't need Lou. They play better with Alan Trammell."
Guillen took his managerial skills to comedic task, pointing out how the White Sox at least split two games back in Arizona with bench coach Joey Cora and Triple-A Charlotte manager Chris Chambliss in charge. Having Guillen and Piniella matching wits, and quips, for the ultimate postseason competition might bring in the Fall Classic's best ratings -- even without the on-field action.
"I'm trying to figure out how they would work that," said Dempster of a Cubs-White Sox World Series. "How you would, as a player, get in and out of the park? There would be nothing like it. It would be bigger than even the Yankee-Met World Series. I really couldn't think of a sporting event of the four major sports to have something like it."
"Every time the Cubs and White Sox match up, and I don't care if it's Whiffle ball, Spring Training or whatever, it's intense," said White Sox left fielder Juan Pierre, who played for the Cubs in 2006. "That's Chicago for you. They are passionate about sports and their teams."
For now, the Cubs-White Sox rivalry brought another spring baseball success to a city known more for its magicians, impersonators and showgirls, who were on display for Saturday's first pitch with Las Vegas mayor Oscar Goodman. But at least one Cubs player gave pause for thought at what this competition would be like with the biggest prize on the line.
"Obviously, it's something you try to imagine, but we're just trying to win the first game of the year," Dempster said. "You envision something like that.
"Anybody who doesn't is lying. It's a long ways away, but at the same time, it sure would be something to see."
Scott Merkin is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.