Being leaders of two of the more powerful cricket nations, Kohli and Smith will be heavily scrutinised. Kohli showed himself to be aggressively minded by instigating a daring chase in Adelaide that barely failed, while Smith displayed a more conservative nature in that series.
However, it would be unwise to read too much into their performance in the 2014-15 series, where both men were stand-in skippers. Now that they have the role full-time, we're more likely to witness something closer to the finished product.
Kohli reinforced the aggressive tag with his positive approach in producing a rare overseas win in Sri Lanka. In an ideal cricket world, where administrators genuinely promoted the charms of Test cricket, they would have gleefully trumpeted the many attributes of Kohli's captaincy.
Not only is Kohli's brand of leadership good for the fans, he's on the right path to improving his team. By challenging the Indian side to play for an unlikely victory in Adelaide, he appealed to the competitive nature of his better performers and also sought to unearth those who could hold their nerve in the hunt for victory. Constantly playing in pressure-packed situations is the best way for good players to improve and to find out who can and can't cut it at that level. Kohli is also fulfilling a prime task for a captain by making the cricket interesting for his players.
"By challenging the Indian side to play for an unlikely victory in Adelaide, Kohli sought to unearth those who could hold their nerve in the hunt for victory"
The highly combative Pakistan skipper Imran Khan once said: "To be a good captain you have to understand bowling."
That's another attribute Kohli displayed in his shrewd handling of the spinners against Sri Lanka. To take India to another level, he has to unveil similar traits in handling the faster bowlers in places like Australia and South Africa.
If Kohli can contain his fiery nature - as he has done so far - and make his aggression work for him rather than against him, he'll become one of India's better leaders.
In trying to gauge Smith's potential as an international captain, it's worth following his upward graph as a player. His improvement as a batsman in the last 18 months has been dramatic and indicates a good cricket brain fuelled by personal pride. That's a good start to successful captaincy.
Based on Imran's theory Smith has another advantage in that he started his Test career as a legspinner. I hope he doesn't forego his bowling, as his potential to break annoying partnerships is a valuable trait.
The biggest breakthrough for a captain is understanding that all the Ws and Ls go against your name. Once that concept is grasped, you captain on your terms and have a legitimate chance of being a good leader.
This will be Smith's biggest challenge. Australia have a huge support staff and Smith will need to memorise the phrase "Stay out of the cricket side of the business", so that he restricts his sources of advice to those who are going to improve the team's chances of winning. Mark Taylor was a very successful Australian captain and his initial act in the job was to let the coach know that the captain was running the show.
There has been an enormous turnover of Australian players following the Ashes loss, but this is not necessarily a bad thing for Smith. He is now in charge of his team and not Michael Clarke's leftovers.
Smith has the opportunity to mould a team in his own style, and the inexperienced Australian batsmen need look no further than their captain for an example of what is required to be successful in Test cricket.
As two of the premier batsmen in Test cricket and captains of strong nations, Kohli and Smith are going to lock horns regularly. If what results from those battles is more Tests like the exhilarating contest in Adelaide, it can only benefit the longer version of the game.