First Nations warriors were actually at an advantage fighting in their style. They knew the terrain and how to fight in the North American forests - most of Upper Canada in particular was heavily wooded at the time, though it's largely been clear-cut today to make way for farmland if you're anywhere south of Muskoka.
The numbers Tecumseh was throwing around aren't all that there were, mind; the British had an entire department dedicated to sending contractors up into the north of the Canadas to hire bands of First Nations allies and bring them south to join the war. It's why you had situations like the Kahnawake from Quebec fighting down in Niagara during the War of 1812, usually under the command of an Indian Department staffer. The British would pay them with a cut of the spoils taken from the enemy armies and that would be that. On balance it was less expensive for them than maintaining large numbers of regulars, though there were always some Redcoats in the area.
It's also not true the First Nations didn't have any modern equipment. They may not have had Redcoat-standard stuff but they did have guns.
I can mostly speak to 1812 and the First Nations experience there, but really, especially in calendar year 1812 and early 1813, First Nations contractors and the small number of British regulars on the scene were the ones doing most of the fighting, and the First Nations groups scored some important victories, often by ambushing the Americans or otherwise attacking out of the wilderness. Because of how they fought, they would sometimes rout or capture the entire American unit with minimal casualties on their side - see also Beaverdams, when 300 Kahnawake and 100 other Mohawks ambushed 600 Americans and took almost the entire unit prisoner while only losing about 10 guys.
The other thing here is, the First Nations seriously terrified the American militia for, basically, racist reasons, which the British played up. Again going back to 1812, there's a point in the battle for Fort Detroit where Isaac Brock literally sent Hull a missive threatening that he had a large army of natives attached to his force and he'd lose control of them once the attack started.