They are two very different characters, with two very different campaigning styles.
"Everything about Sunak's approach is slick," says PR expert Mark Borkowski.
"It is overly professional in some points. I am not sure whether that is a good or a bad thing. There seems to be a lot of strategy and thinking behind it."
The Truss campaign on the other hand "feels a little bit more homespun", he adds.
Sunak's social media strategy is masterminded by Cass Horowitz, son of best-selling novelist Anthony Horowitz. As a special adviser to Sunak when he was chancellor, Horowitz used fancy graphics and clever tag lines to sell "Brand Rishi" to a younger, politically unengaged audience on Instagram.
The glossy "origin story" video Sunak used to launch his leadership campaign on Twitter - in which he talked about how his mother came to the UK in the early 1960s "armed with hope for a better life" - has been viewed more than 8 million times.
So slick was this film that it raised suspicions that it had been in the works for some time - a
suspicion shared by Mark Borkowski, who notes: "You don't create this sort of campaign overnight".
Team Sunak insist the video was put together in 24 hours, after Boris Johnson announced he was standing down.
Liz Truss's social team, run by Reuben Solomon, former head of digital at the Conservative Party, and a protege of Boris Johnson's favourite election strategist Sir Lynton Crosby, have played it safer so far.
The foreign secretary's launch film is an attempt to project her as an international stateswoman. There is little about her own back story, and no spontaneous "behind the scenes" footage. There is much talk about "delivery".
One similarity between the two candidates - and indeed all of the Tory MPs who threw their hats into the leadership ring - is their desire to be on first name terms with the electorate.
This is not a smart move, according to Anthony Ridge-Newman, associate professor of media and communication at Liverpool Hope University.
"Boris Johnson is one of the few politicians to ever be referred to commonly by his first name. The online campaign slogans, both Liz for Leader; and Ready for Rishi, are an attempt to emulate Boris's first name appeal.
"Had either of the Tory leadership candidates come to me for my expert advice, I would have suggested foregrounding their last names, Sunak and Truss.
"It would help their campaigns appear more prime ministerial, which, if I know anything about the Conservative Party, is something they look for in their candidates."
Rishi Sunak's use of video has been more adventurous, with candid, supposedly off-the-cuff footage of him reacting to key moments. There was even an unexpected venture into comedy, with a parody of 1930s cinema newsreel, in a video trumpeting his Brexiteer credentials.
But neither candidate is a natural in front of the camera or the smartphone, in Ridge-Newman's opinion, lacking the fluency of Boris Johnson or David Cameron.
"Sunak's digital content is largely presenting him to be a regular guy," which may be an attempt to neutralise recent media portrayals of him as a member of the wealthy "elite". he says.
"Truss on the other hand is presenting herself in a more statuesque manner. The digital content comes across quite posed and generic, and plays on her role, time and successes as foreign secretary.
"While Truss does not come across as a digital native, her social media campaign seems as though it is most strategically steered towards the Conservative Party membership, who are the ones who will be voting to decide Britain's next prime minister."
One problem for Team Truss is that memes making fun of their candidate have been shared far more than anything produced by the campaign.
"She seems to be the one suffering from a lot of parody," says Mark Borkowski.
So far, Google searches for "Liz Truss" have far outranked those for "Rishi Sunak", but they are often accompanied by the word "cheese".
This is a reference to a 2015 conference speech. in which he she says, in an impassioned voice: "We import two-thirds of our cheese. That. Is. A. Disgrace."
Mr Sunak has also attracted derision on social media, with Labour supporters and others sharing a clip of him as a teenager talking about how he has no working class friends.
But ultimately this is not a campaign that will be won and lost on social media.
As the BBC's Media Editor Amol Rajan has pointed out, the Tory membership are "a narrow section of the population that is much more attuned to newsprint than most Britons".
And Liz Truss appears to have one of the UK's biggest-selling papers The Daily Mail in her corner, which could prove decisive for her.
"In this old-fashioned newspaper election, the tenor of newsprint coverage over the next week could have a significant impact on who becomes prime minister - especially if the Times, Sun and Telegraph decide that, like the Mail, they know who they want, and give hell to whosoever they decide they don't want," says Amol Rajan.