The Uruk-Hai carrying Merry and Pippin were hampered by the heavy armor and arms they were wearing and carrying.
Thus, Legolas, who was wearing no armor and lightly armed, should have been able to overtake them.
However, Legolas refused to leave his companions, Aragorn and Gimli, behind, and they could not keep up with the Uruk-Hai (and Gimli was heavily armored and armed, which further hampered the situation.)
Legolas could actually run in his sleep. This is expressly stated in the book. If Legolas could do so, so could all of the Wood-Elves.
And if Wood-Elves, the Nandar, could pull this kind of stunt, there is little question as to what the mighty Noldor could accomplish.
I would say Legolas could easily make 100 miles per day, every day for at least a week straight.
Par for the course for Wood Elves.
For the Noldor, much greater distances are probably possible. Maybe 200 miles per day. Or even 300 miles per day.
The Uruk-Hai, capable of running in sunlight, could at the very least equal the Wood Elves (if armed and armored, they could match armed and armored Wood Elves. If lightly armed and unarmored, they could match lightly armed and unarmored Wood Elves.)
The Orcs of Mordor could and did function during the day (witness Grishnakh and Company.) Although the sunlight undoubtedly bothered them, it did not seem to hinder them much.
I'd give the Orcs of Mordor 7/8ths the speed of the Uruk-Hai.
That is, they could match the Uruk-Hai at night, and almost match them during the day.
The Orcs of the Misty Mountains are another matter.
Sunlight impairs them badly. They can run in the sun (as shown in the book) but they are greatly slowed and long term exposure is injurious to them.
I would give them 3/4 of the speed of the Uruk-Hai. That is, they can match the Uruk-Hai at night, and run half as fast during the day.
Over a several day period, their performance would drop to 1/2 that of the Uruk-Hai, as their increasing exhaustion led them to slow down at night, and during the day practically coming to a standstill.
Dwarves and elves both seemed to have the capacity to run at incredible speeds, over short distances.
By incredible, I mean pushing well over 15 miles per hour. Perhaps approaching 20 miles per hour in spurts. (Thorin and Company's flight from the goblins in The Hobbit comes to mind here.)
The In Real Life World Record, by the way, is 21 miles per hour for the 50 Yard Dash.
All Orcs and Uruk-Hai have this same capacity for incredible spurts of speed over short distances (the Orcs of Moria outran Thorin and Company.)
It is implied that elves can slightly outmatch dwarves also, in this regard.
Therefore, if your side is human, hobbit, or dwarvish, and the other side is elvish or orcish, and your side routs, you might as well say your prayers.
You aren't going to get away.
You cannot outrun the elves (or orcs) in a sprint.
You cannot outrun the elves (or orcs) in a long term race.
Elves (and orcs) tend to be tenacious, and have this bad tendency to hunt down their enemy to the last and least.
If you can purloin a horse, you will get away ... maybe. An eagle would be better.
There is one beast in Middle Earth faster than any elf or orc. This is the balrog.
Balrogs are amazingly fast.
How fast? Try Freeway Speeds, or faster (that is, do not try to outrun one in your Middle Earth SUV on the Middle Earth Freeway, for you will lose the race.)
If Gandalf had not stopped the balrog in Moria, it could have been at Caras Galahon within the hour (and then someone would have had to stand up and fight it. Not so good for those people ...)
Indeed, there is some question as to whether even the eagles could outpace that balrog.
An immensely valuable ally for Sauron it would have been, once the War started, had it still been around (and assuming it bothered to answer Sauron's call for help, which is questionable.)
- - -
It should be remembered that sheer prowess in battle was not the final worth of someone in combat in the War of the Ring.
The Noldor had the greatest Stature, and this translated into immense combat capability. A single Noldor was worth dozens of men in combat.
The Sindar and Nandar had the next greatest Stature, and this translated into improved combat capabilities. We see this, to some extent, in Legolas, Haldir, and the Army of Lothlorien.
The Orcs of Mordor were next.
For Sauron put his own power into them. As a Fallen Maia, he put his power into them, giving them greater combat capabilities than they should have had.
(Saruman could not do this for his Uruk-Hai. Saruman was not a Maia on the power and level of Sauron.)
The Dunedain of Gondor, and the Rangers of the North (also Dunedain) were greater in stature also, compared to ordinary fighters. The descendents of Numenor had a remnant of the blessing of the Valar still within them, and could pull off feats others could not (such as taking the road of the Paths of the Dead, and getting away with it. Or surviving in the wilderness for decades on end, as Aragorn boasted about to Sam at the Prancing Pony.)
Dwarves and hobbits comprised the next most combat worthy peoples (although it had atrophied with hobbits.)
Finally, we come to ordinary men, such as the Rohirrim, the non-Dunedain people of Gondor, the Haradrim, the Corsairs of Umbar, the Easterlings, the men of Lake-Town and Dale, the people of Dorwinion, and others.
On about a par with ordinary men were the lesser orcs, the Snaga, such as those found in the Misty Mountains and in other places.
The Ents are a special matter, as are trolls.
Both are quite combat worthy (a point well shown in the films!), but it is heavily due to size and strength, and Stature seems to have a lessened role here.
Trolls were supposedly bred in mockery of Ents, just as orcs were bred in mockery of elves, if you believe one version of Tolkien.