We actually have seen Stannis in battle, on many occasions actually.
First off, we have the Siege of Storm's End; in-which he held out for over a year against the forces of Mace Tyrell. Now, you would say that a siege does not count; or that this one has no purpose in the matter of command, but it really does. This is because of the fact that Stannis did not submit, even though the majority of his men wished to. Even with a substantially lesser army than the hordes of the Reach. Stannis managed to keep his men in-line (which is a big thing for an untested commander of nineteen years), hold out against the army of the Reach (though you would say that Mace Tyrell is a ludicrous commander himself, Mace had the aid of other great generals like Randyll Tarly, Paxter Redwyne and others); through this Stannis intentionally kept the Tyrell army out of the war, basically serving Robert his victory.
Secondly, Stannis' victories during the Greyjoy Rebellion. Not only did he crush the Greyjoy Fleet at Fair Isle, he took Great Wyk with less men than the other commanders, and in the fastest time; also that fact that Great Wyk was the largest and most defended island of the Greyjoys. The Battle of Fair Isle, was a master stroke by Stannis. Not only did he have less ships and men, but he defeated a seasoned commander: Victarion Greyjoy. Luring the Ironborn fleet into a trap, he descended upon them and 'dealt Victarion his most crushing defeat' (ADWD, Victarion Chpt. 56). Destroying the Greyjoy's primary advantage, seapower. Siege of Great Wyk, Stannis assaulted the island and defeated the major pocket of Greyjoy resistance; taking the isle before the walls of Pyke had been breached.
The War of the Five Kings. Though Stannis had made bad decisions during the Siege of King's Landing, it was to be said that he was on the verge of breaching the walls before Tywin arrived. Even without Melisandre, Stannis had instilled fear and lowered the morale of the Lannister defenders; mainly in the point of routing Sandor Clegane, and Joffrey fleeing did aid either. Tyrion's sally was not as effective as many say, even before he is injured his men begin to waver.
Now, though Stannis was not loved; he is Respected and Feared. He is also a very inspiring leader. After the Wildfire, he managed to rally his men to take to the walls. During the Siege of Storm's End, he kept an entire garrison stay strong. Even after his defeat of King's Landing, he kept control and led them North; despite many believing him insane. Stannis is considered to be, even stated by Martin himself, the Greatest Military Commander in Westeros. Characters like Varys and Tywin, behold that opinion of him.
Robert, being a great warrior and a fierce fighter, would not win so easily as you think. Robert is inspiring, respected and loved. But some of his actions of the field are questionable. His battle of Summerhall was an victory, though he did have the upper hand and the larger force. At Ashford, his larger host was defeated and routed by only the van of Randyll Tarly. Though we have the Bells, Robert's participation in it was vague and cannot be used as evidence for command; due to being in hiding for it's majority. The Trident, though being Robert's largest victory, his victory only came from defeating Rhaegar. After the Princes' death, the Royalist routed, if he didn't; Robert might of lost. Both armies were of equal size, along with both commanders (Robert having Ned, Jon, Hoster, Jeor and others whilst Rhaegar having Lewyn Martell, Barristan, Bywater and others)
A battle between Robert and Stannis would be evenly matched, both enspire respect. Robert inspires love, but Stannis inspires fear. And we all know fear is more powerful than love in terms of battlefield loyalty (think of Tywin and Robb, Tywin's vassals didn't even debate any of his choices, whereas for Robb, his entire army fell apart). I would say it is a 50% - 50% chance on either side, even with supporters.
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