One thing that's necessary to point out as that Napoleon was held as something of a bit uppity during the earlier Revolutionary Wars.

For instance, he was given command of the Army of Italy not because they thought he would actually defeat the various Italian armies and the Austrian Army, but rather to distract those forces and remove the overly ambitious general from the main event up north. Napoleon had just been made something of a big name with his defeat of the Royalist insurrection in Paris (where we get the dubiously attributed, "whiff of grapeshot," quote) and many were worried about his political ambitions. His Italian Campaign was not meant to be the primary thrust of French forces, though that is what it ended up being. The Rhine campaign was considered the main thrust of the French Revolutionary forces. Thus, it could certainly be said that the commanders Moreau and Jourdan were rivals of Napoleon's, as they were appointed the commanders of this far more important front (Napoleon actually ended up exiling the former in 1804).

Really, Napoleon would have seen just about anyone competing with him for power, prestige, etc. as a rival. He was a very ambitious man and found allies where he could, but also understood that some men stood in his way. For instance, Jourdan was later made a Marshall of France. He saw a road to where he wanted to go and didn't let anything stop him on his path. Even early on at the Siege of Toulon there's reason to suggest that he was only given leave to attack in order to get rid of him. I'd certainly think that this could constitute something of a rivalry between Napoleon and the commander of those forces.

I'm at work, but let me know if you'd like some specific sources or have more questions.

The First Total War by David A. Bell covers most of what I've been talking about.

The answer partly depends upon what one means by "rival."

Being a general in Republican France often meant more than just success on the battlefield, it was also a highly politicized occupation. This was doubly true during and after the Terror when personal connections and an ability to navigate the corridors of French politics were essential skills for any flag officer. Although subsequent Napoleonic mythmaking and propaganda would emphasize his own rising to the top of the greasy pole as a fait accompli in Brumaire, Napoleon was only one of several popular generals that various conspirators within the Directory were hoping to use to kill off the existing French government. Emmanel Sieyès, one of the key plotters in Brumaire, would famously quip, "I need a sword," in other words, a man who could command the loyalty of one of the few powerful institutions that possessed a great deal of popular legitimacy within the Republic, the army. Bernadotte, a general and Minister of War, was the favorite of the Neo-Jacobin factions that wanted to reestablish the Revolution's leveling tendencies. Jean-Baptiste Jourdan toyed around with many different factions. Lazare Hoche, who enjoyed almost as much fame as Napoleon had unfortunately died of tuberculosis before Sieyès's initial soundings towards him could bear fruit. Jean Moreau, the youngest general in the army, refused to compromise himself with politics despite entreaties to do so.

In terms of tactical and martial skill there were certainly a number of rising military figures in the Republican army that at times managed to match Napoleon's drive and determination to achieve victory. Hoche symbolized the Revolution's leveling tendencies perhaps more so than Napoleon. Hoche, a scion of a poor family rose from the ranks and managed to win a series of victories against the Austrians and Prussians in Germany. Like Napoleon's whiff of grapeshot, Hoche too engaged in military activities that seemingly saved the Republic such as his 1795 destruction of Royalist landings in the Vendée. Similarly, Moreau was another young turk in the Revolutionary Army. He had won a series of victories in Germany and was the youngest general in the army at the time of Brumaire. Jourdan was another general whose fame stemmed from the German front. Although French armies in Germany did not accrue the same level of victories as Napoleon did in Italy, this was the theater that France identified as the main strategic center of gravity for French arms. Napoleon rose to national prominence in 1796/97 in part because the French campaign in Germany fizzled out.

Jourdan became one of the first crop of Napoleonic Marshals. The Marshalate included a number of figures who had an uncommon degree of skill and determination that was on display in the Napoleonic Wars. André Masséna was one of Napoleon's chief lieutenants in Italy and would later prove himself to be one of the few Marshals capable of independent command. Masséna's actions in Switzerland in 1799 and the Siege of Genoa in 1800 showed that he was resourceful when faced with superior numbers and capable of inspiring his troops to perform a series of marches and countermarches as he did in Switzerland when he faced off against two of the age's foremost generals, the Russian Suvorov and the Austrian Archduke Charles. Likewise, Louis-Nicolas Davout proved to be one of the most steadfastly competent military commanders of the age. He was a Republican veteran of the Rhine campaigns and although he was never a loved figure in the army, troops under his command were drilled mercilessly. Davout's likely took his marshal's baton in place of his departed friend Louis Desaix, who was responsible for saving French arms at the Battle of Marengo.

In a roundabout way, Napoleon's treatment of Desaix, who died at Marengo, indicates the degree of martial skill the latter possessed. Napoleon had arguably lost the Battle of Marengo, but Desaix's arrival had reversed French fortunes. But Napoleon minimized the efforts of Desaix in Marengo and tended to exaggerate his own military sagacity. Napoleon's Bulletins and reports from the front likewise did not pay much heed to the fact that Masséna's conduct at Genoa had allowed Napoleon's army considerable freedom to maneuver during the campaign. Davout's achieved his greatest victory at Auerstadt while commanding a single corps that destroyed the main Prussian army. Napoleon at Jena refused to believe that Davout had achieved this feat and while acknowledging Davout's victory, insisted that Auerstadt be linked in all correspondence with Napoleon's lesser victory at Jena.

This tendency of Napoleon to usurp all of the military glory certainly rankled among many successful officers of the Empire. Masséna bought an estate upstream of Napoleon's residence of Malmaison and reportedly liked to urinate in the stream that fed his master's residence. Davout for his part served ably and loyally, but Napoleon's postwar reminisces of him at Saint Helena often damned the Marshal with faint praise. Although Napoleon rewarded military successes lavishly, he would never acknowledge the existence of military rivals.