Hmm. I can see a few 20k+ armies for Rome before even looking at the civil war where they fielded huge armies - Medway is one example - where as battles like Cerignola and La Motta are around 10k a side.
Hmm <cracks knuckles>
Okay I just picked a war at random: The War of the League of Cambrai 1508-1516:
I lowballed all the numbers to get the average if I was given a range
Agnadello 30,000 v 15,000
Padua (siege) 40,000 v 15,000
Brescia (siege) 12,000 v 15,000+
Ravenna 23,000 v 21,000
Novara 22,000 v 11,000 - 20,000 (unknown exactly how many swiss)
Battle of the Spurs 30,000 overall (but many fewer were engaged) v 7,000
Flodden 26,000 v 30-40,000
La Motta 13,000 v 9,000
Marignano 30,000 v 22,000
Average size of army: 20,611
Tbh, I suspect a well led Roman army could beat a poorly led Napoleonic era army. It's not like we don't see massed infantry break foes in melee in this period, and well trained archers and slingers would be a very nasty surprise for unarmoured outranged infantry. I'd also point out that Napoleonic era artillery is still firing only two roundshot a minute...
Technically I do think a man with a rifle and a bayonet has the advantage over one with a sword, never mind how many shots he got off before the roman could get within arms reach - the longer reach of the bayonet is a significant advantage- Lindybeige did some interesting videos on how one-on-one a spear usually beats a sword. True in a mass melee, this advantage does get cut down a lot. But with proper bayonet drill - hence me pointing out Culloden, where the government forces had to deal with highlanders who relied on shock tactics and getting close and personal with swords and dirks - it can continue to be relevant.
Re: the cannons, I was thinking about the small light field cannons of Gustuvus Adolphus - '3 pounders' I believe - who had a firing rate 3-5 times more than the heavier guns of the opposition. Also they were pioneering canister shot. I don't know when they went out of favour nor do I know if that means they were firing 6-10 shots per minute. (10 per minute certainly seems to be the max allowed if you have 6 second cycle.)