As well as competing for trophies at club level, the pair are also battling it out for a starting spot at international level with England.
If there is still room for improvement for Wan-Bissaka in terms of the attacking aspect of his game, the same is true of Alexander-Arnold in a defensive sense.
Here, Sports Mole looks at how the duo compare using stats from the 2019-20 Premier League season to date.
Firstly, it is worth noting that Alexander-Arnold has made three more appearances than Wan-Bissaka in the English top flight this term.
Given he plays for the side boasting the best defensive record in the division, it is not surprising to learn that the Liverpool defender boasts more clean sheets - 10 compared to seven.
In terms of goals conceded, United have let in 28 this season with Wan-Bissaka on the field, while Liverpool have shipped 21 when their own English full-back has been present.
Many will argue that the job of a defender first and foremost is to keep out the opposition. In Wan-Bissaka, United have one of the finest tacklers anywhere on the continent - especially in one-on-one scenarios.
His 99 tackles won is the second best return in the Premier League, bettered only by Leicester City's Ricardo Pereira.
Wan-Bissaka also ranks highly for interceptions and aerial battles won, though he comes out second best to Alexander-Arnold in terms of general clearances.
The role of the modern full-back is constantly evolving, and many will argue that attacking is now just as important as defending.
That is where Alexander-Arnold comes into his own, scoring twice in the Premier League this season from 36 shots, eight of those on target.
Both of those goals were scored with his right foot, one from inside the box and the other from outside.
Wan-Bissaka gets into shooting positions far less often, managing only one shot on target from his five overall attempts, failing to find the back of the net from any of those.
Goals are a nice bonus, but assists are the bread and butter for Alexander-Arnold.
Twelve times he has set up a teammates to score this term - second in the division to Manchester City's Kevin De Bruyne - while Wan-Bissaka lags well behind on two assists.
Alexander-Arnold also performs better than Wan-Bissaka in terms of passing - especially when it comes to forward passes - and touches of the ball.
Where Wan-Bissaka particularly falls short is in terms of crossing, sending in wide deliveries on 75 occasions in 2019-20. To give that some context, Alexander-Arnold has swung in 313 crosses.
Neither player has yet been red-carded this season, while Wan-Bissaka's five yellow cards is one more than Alexander-Arnold has been shown.
Ultimately, though, this comes down to whether you want your full-back to keep out opponents or create chances.
Combine the two aspects, and it is Alexander-Arnold who leads the way.