Actually Kirkenes and Tromsø are similarly far north, Kirkenes is at 69, 43' N, and Tromsø is at 69, 40'. However, Kirkenes is much farther to the east, and thus appears to be further to the north on most maps. Alta is slightly further to the north, at 69, 58'.
Honningsvåg (the airport closest to the North Cape) is the northernmost in mainland Norway at 71, 0', but the village is not that interesting, especially in autumn. Hammerfest is the northernmost city of Norway (and for tourist purposes: in the world) and is at 70' 40'. Be aware that the latter two are only served by Widerøe, using Dash-8's. A change is necessary at Tromsø, and flights are much more expensive there. Choosing between the two, I would definitely go for Hammerfest (I am actually going there on business in a week's time), but for the OP's purpose, I would go to Tromsø.
I would not necessarily expect much snow even in late October. As for the aurora borealis, you might have luck, and then you might not.
Thanks a lot for the info. I am now more interested in Tromsø. Should I rent a car or join a tour if I want to chase the northern lights at night?