Whereas ARC troopers are infiltrators and commanders outright, clone commandos are literally walking tanks in every way, and so nothing can really be said other than that clone commandos are better by a long shot, but given very little opportunity to prove that to the fandom unfortunately. Advanced Recon Commandos, also known as ARC troopers, were an elite variant of the clone troopers that served the Galactic Republic. Chosen from the ranks of the Grand Army of the Republic, the status of ARC trooper was bestowed on clones who served with distinction on the battlefield, such as Echo and Fives.
The training of clone cadets also served as a means for identifying particular cadets. ARC Troopers and Clone Commandos are two highly skilled groups of soldiers, but what exactly is the difference between the two? Are the Bad Batch Clone Commandos? And how are commandos different. The Grand Army of the Republic is fed up with fielding two different sets of Commando Forces and decides that one of the two must go in an effort to standardize the Republic's Commando Forces due to another attack on Kamino which decreased the amount of cloning cylinders available.
As a result, the GAR pits four ARC Troopers versus four Clone Commandos in a fight to the death. One the ARC side. What is, in details, the difference in the type of mission assigned to ARC Troopers, Clone Commandos, Spec Ops Troopers (see 2nd Battle of Geonosis), ARF Troopers and Clone Scout Troopers (see Battle of Kashyyyk)? Reading their description, they seem to all involve recon, infiltration, missions behind enemy lines, etc.
ARC are "Advanced Recon Commandos", what exactly do they do that Commandos. ARC Troopers commonly customized their armor for identification purposes and were known to have intricate designs on their equipment, particularly their kamas. Traditionally, like standard Clone troopers, the color of an ARC Trooper's armor depended on their rank.
However, this practice was abolished as the war progressed. In terms of design, I personally prefer the look of Arc Troopers (partially because they were allowed more customization than that of the commandos, and especially that of standard clones. Are ARC Troopers or Clone Commandos more skilled/capable? I've always made it in my head into: ARC troopers are the sort of Rangers of the modern US Army, while Clone Commandos are the Special Forces like Delta Force.
I think it really depends on the clone specifically I'd wager Rex could take on any Commando but on average it seemed commandos were more selective and used in special ops, whereas ARC troopers were decorated as the best and most capable of the regular troop population. Clone commando's, by comparison, were deemed capable of pulling off in teams of four what a single ARC could do. The drawback being each commando generally specialized in a different task (ie one leader, one tech/hacker, one demolitions, one sniper) so you needed all of them together to pool their skills to pull off similar stunts.