I agree with von Adler regarding Swedish superiority in numbers and artillery, while the terrain would favour the defender, which would be Norway.
But there are some points which taken together would, I think, favour Norway:
Norway would be the defender and need only put up such a fight as making Sweden feel it's not worth it to fight to keep a hostile Norway in the union. If Norway was able to survive the initial Swedish onslaught, this point would come quickly. 90 years of Norway doing almost everything it could to frustrate Sweden had made Sweden weary of trying to keep the union going. Sweden would not relish the prospect of continuing to try to keep the union running after a military victory which would have exhausted both countries. In fact, the moment Sweden accepted that its overlordship over Norway in 1814 was to be as the dominant partner in a union, instead of just incorporating Norway, it gave up the notion of Norway and Sweden as one country. It was only a matter of time, I think, before the two countries would break up.
Whereas USA could afford to fight an existensial war to keep the union, having no major security threats from abroad, Sweden could not afford this. Being a medium European power at the turn of the last century meant having to be always on the alert for foreign threats. I don't think Sweden could afford to be involved in a civil war. It would always have to be wary of how the neighbours could exploit the situation.
Also, I think the military forces of Norway and Sweden where more evenly matched than one might believe. Sweden was superior in numbers and artillery, but Norway's new army was more modern regarding small-arms, in particular machineguns. The devastating effect of machine guns in defence would only be really internalized during WWI, so Sweden would not take proper precautions against the Norwegian machinegun-manned defensive positions. So the initial Swedish attacks would be very bloody. Due to the terrain and population concentrations, the Swedish attack would be very easy to foresee. These attack-routes was heavily fortified. Norway had been building fortifications in the south-east since 1884.
If Sweden wanted to avoid these, it would have to cross the border further north. But there was only mountain-passes and highland plateau's with almost no people and extreme weather and temperatures. When Arnfeld attacked from Central Sweden through to Trondheim a couple of hundred years before, he met almost no resistance. But being unable to survive wintering in Trondheim, he had to retreat. But his entire army of 3.000 died of the sickness and cold, as the snow lies all the year in the passes.
So I think the end result would be an independent Norway, two economically devastated countries (but with Norway probably being able to handle this better, since it would be fuelled by nationalism and a sence of victory), all sorts of major power positioning and messing about, and maybe a bit different WWI, as the superiority of the defence might be better understood.