For one thing, Duverger's law would likely be ineffective, meaning that there would no longer be a convergence to two parties in FPTP system.
This is because, typically, the way Duverger's law works is, by forcing people to excercise tactical voting by voting for whichever of the 2 main party candidates they find least objectionable. This is because voting for a minority 3rd party candidate they actually like - effectively counts as 1/2 vote for the major-two candidate they dislike more. So, Perot voters helped elect Bill Clinton (or so goes the popular narrative), and Nader voters helped elect G.W. Bush (also a popular narrative that, actually, was disproved if you look at the numbers). But the truthiness of the narrative is irrelevant - only the level of influence the narrative has on voting behavior.
However, if you can downvote a candidate, you can now downvote the major-two candidate you dislike more instead of upvoting the one you dislike less. This will not affect the balance between major candidates (since a downvote for A is same as upvote for B, in the balance between the two) - BUT, a downvote for major candidate A is also effectively an upvote for 3-d party candidate C!
As such, in elections where a large portion of electorate isn't terribly inspired by either candidates, and mostly votes for "lesser of two evils" in current FPTP, the two major party candidates just might accrue enough down-votes that a 3rd party candidate who isn't nearly as disliked will, on balance, win over both of them (or at the very least, acquire more than the abysmal 4% combined popular vote and 0 electoral vote like 2016 US presidential elections, despite 3rd party candidates combined likely being preferred by 40% of electorate, as a low bound).