Grishnakh is an Orc of Mordor, and more specifically of Barad-dur itself. He is short, crook-legged, almost apelike. This gives us the immediate impression that, unlike the tall, solid Ugluk, Grishnakh is unlikely to be a battle-line fighter. Instead, we can see him as exactly what he is: a raider, skilled at slipping into places, sneaking around, and killing without being seen.
Grishnakh is fairly high-ranking; not only is he leading a large group of Orcs on an independant assignment a long way from Mordor, he also seems to know about the One Ring - and recognises Merry's imitation of Gollum. Whether he was given this information, or obtained it for himself by eavesdropping, it is clear that he spent time actually inside Barad-dur.
Most interesting, in light of the later conflict between Shagrat and Gorbag, is that Grishnakh professes admiration and loyalty to the Nazgul. We know that even between the close-together towers of Minas Morgul and Cirith Ungol, the orcs saw each other as bitter rivals. It's hard to imagine Grishnakh, back in Barad-dur, speaking kindly of Morgul orcs. However, we see him putting on a united front for outsiders: against the goblins of Moria and the orcs of Isengard, Grishnakh will defend even his sworn Mordorian enemies. It would have been interesting to see how he treated forces out of Dol Guldur - another of Sauron's direct commands, but outside Mordor proper.
In Ugluk, we see a stark contrast to Grishnakh. While the Mordor orc comes across as brash, almost impulsive, Ugluk seems almost an 'elder statesman'. He, alone of his company, understands the dangers of allowing a Rohirric scout to go free, and he is a skilled enough fighter to duel Eomer hand to hand.
And he knows it. As he is fond of declaring to his 'northern rats' - "We are the fighting Uruk-Hai!" In the books, that doesn't mean he's a separate species - 'uruk' simply means 'orc', and 'hai', 'folk'. Ugluk is claiming, in effect, that his people are the only true orcs. He says it with the pride of the one who shaped them to be what they are - of an orc who clawed his way out of the mass of the likes of Grishnakh, and created a company of true warriors. He may not be their father, but they are his 'lads' nontheless. In the service of Saruman, who feeds them on man-flesh, Ugluk has fulfilled his potential as a warrior.
Ugluk dies in a hand-to-hand duel with Eomer. Why did Eomer do that? Is it possible that he recognised this particular leader of the Uruk-Hai? Is it possible, in fact, that Ugluk was responsible for the death of Theodred at the Battle of the Fords of Isen? Or, indeed, the murder of Eomund, Eomer's father, back in T.A. 3002? Is Ugluk not just an orc, but the orc - the one Eomer has been hunting his entire life?
So how old is Ugluk? Tolkien was notoriously undecided on what, exactly, Orcs were, so the best way to answer this is to look for other examples. Bolg, son of Azog, reigned as king of the orcs of Moria from his father's death in 2799, to the Battle of the Five Armies in 2941 - some 150 years. We can certainly assume he was already a full-grown, experienced warrior at the start of his reign (orcs not being noted for their loyalty), and that he still had a good few years left in him at his final battle (or else he wouldn't have been able to fight). So let's assume an orc can live at least as long as a dwarf - around 250 years.
Knowing that, we can see that Ugluk clearly didn't begin in the service of Saruman - while already corrupted, Saruman only fell under Sauron's direct control around T.A. 3000, when the Dark Lord returned to Mordor. Nineteen years seems just a little young for Ugluk. The idea that he might have been sent to Isengard by Sauron doesn't hold up to Ugluk's obvious scorn for Mordor.
There is an answer, and it lies on the literal White Hand. Saruman originally opposed the idea of the White Council attacking Dol Guldur because he thought the slow rise of Sauron would prompt the One Ring to reveal itself; he later agreed when he realised Sauron might know where the Ring had actually been lost. His fascination with Rings of Power was already well engrained - and so we might assume that he had already tried to make his own.
With the fall of Dol Guldur, Sauron fled to Mordor. There is no word of what happened to his armies; many were no doubt destroyed, but could one Ugluk, then a raider much like Grishnakh, have retreated into the woods? Abandoned and betrayed by the Dark Lord, he could have remained there, watching, as Saruman hunted through the ruins - and, indeed, as the White Wizard forged his own, weaker but still potent, Ring. We know that the voice of Saruman was a powerful instrument of control, even before he wore a ring; augmented by his creation, might he not have seen the 'wisdom' in creating an army of his own? And could he not have called the abandoned orcs out of the forest, bringing them down to Fangorn and Isengard long before Sauron claimed him?
We might even imagine that Saruman had a 'noble' purpose in mind. He took Ugluk and his lads, the scheming, squabbling, hunchbacked, treacherous orcs of Sauron, and - through training, through control, maybe even through magic - helped them remake themselves into tall, disciplined warriors. Surely, this was an act of good! Saruman was redeeming these orcs - taking their malformed state and turning them into true warriors - the only real orcs in Middle-earth - the fighting Uruk-Hai!
Somehow, I don't think Gandalf would have been convinced.