You say this is in the Napoleonic era, eh? Well, I know a thing or too about that.
Intel
Ultimately, intel in the middle of a battle of this scale is of little use. While scouts, spies and intel did play an important role in the Napoleonic wars, this was mainly on a large scale where armies would try to out maneouver their opponents for long periods of time, constantly weighing up their opponent for a sign of weakness. In a battle of 200 people, a leader would be able to stay close enough to his troops to react to problems as they arose.
However, knowing the plan of attack of the enemy would be useful, as a suitable counter would be devastating against certain attacks in the Napoleonic era.
Training
Now really, it depends on what kind of training this is. For the common musket-armed soldier, accuracy took a back seat to fire rate. The best soldiers were those who could reload and fire the fastest. Soldiers with superior marksman skills were assigned rifled muskets, but since those presumably come under the heading of 'Equipment', we won't have those. In a straight up fire fight (two firing lines opposed to each other), the superior fire rate gained from better training could help.
Equipment
As noted above, the key 'weapon upgrade' of the Napoleonic was the rifled musket, which took longer to reload but was far more accurate. It's hard to say whether this would be a worthwhile choice, as it really depends on what the army has as basic and what the superior equipment would be. Bayonets would be a necessity to implement a 'cold steel' attack (aka a bum rush), for example.
Supplies
Superior supplies are of little value if the army doesn't have somewhere to hunker down with them. Taking a purely defensive stance on an open plain would be inadvisable, as it would allow the enemy to flank and surround us. Supplies were a key concern for Napoleonic generals due to the difficulty of long distance supply lines at the time, which was why Napoleon implemented the technique of 'living of the land'. Although trying to eat scavenged local food didn't work out too well in Russia...
What I'm saying is is that supplies are ultimately irrelevant in a small battle which will probably be over in an afternoon (assuming we can find the enemy in this fog).
Number
Outnumbering the enemy two-to-one would be a collossal advantage in the Napoleonic era. Number mattered then more than ever; you would have more troops firing shots, a greater possibility of outflanking the nemy or surrounding them, and the sheer psychological effect of an onrushing horde of soldiers can not be ignored. Assuming the troops had bayonets, we could scatter the enemy with a single charge.
Support
Artillery would only be useful against massed enemies; trying to hit the enemy on an open field (which you say is covered in fog) would be almost impossible, even if the cannons had a hill to shoot from (which I assume they don't.
Conclusion
I'd probably go with numbers. Some of the most successful tactics of the period were based around superior numbers, so the extra soldiers would make the army more flexible as well as more powerful.