When he came into power in 2001, the Department of Justice suddenly stopped asking for the breakup of Microsoft, and started suggesting other remedies. There is actually a pretty good chance that Microsoft would have been broken up into a "Windows company" and an "Office company" if Gore instead of Bush had been elected.
You might also notice that the antitrust case against Google in 2011 also began under a Democrat. (Personally, I think the case against Google was a mistake, but that's another topic...) At the end of the day, the facts are that the Republicans haven't been very interested in antitrust lately.