Why don't we list the disadvantage/s of the weapons?
1. Nuclear bombs: the blast can be hidden and the fallout, unless constant bombardment, would clear out in a month or so, meaning that while it might be a good short term annihilation weapon, it is not great for long term life killing. Also, life finds a way, to mutate and thrive.
Nuclear is actually good for long-term death, not because of the fall-out, but because the massive explosions kick up dirt and dust and ash into the atmosphere, similar to a volcano. Throw a lot of them, or a few big enough, and you'll choke out the sun globally, killing all the plant life, and thus the food source for most terrestrial life. Also, while there won't be sunlight for photosynthesis, what there will be is greenhouse effect on steroids, massively raising the global temperature, and that'd kill too.
So, you bomb every major population center, and then maybe a few more just spread out so everywhere is nearby a site, and that should be enough to eliminate most humans. There might be a few that survive in shelters with stockpiled food, so you just have to hope/make sure that the ash clouds stick around long enough that by the time they run out of resources, the surface hasn't recovered. Either by calculating how much firepower you need all at once to make that happen, or by setting up an automated system that occasionally launches a few extra nukes every few years or something.
I'm not sure how the nukes would effect the oceans though. You
want them to suddenly rise in pH a lot, cause that'll kill a lot of the living things in there, and that will make it hard to recover. You might have to set something different up for that. That's assuming you want to wipe out as much life as you can, rather than just humanity. Devastating the oceans' life will make it much harder to source food from them after all the surface plants die, and it will make it harder for life to recover in the long run; if you managed to wipe out all terrestrial life, then life has to evolve to put food back on the land, and then creatures have to evolve to survive on it again.
It's practically impossible to end all life in Earth; there are microscopic organisms built to survive in the most obscenely extreme conditions, and no matter which of the above doomsdays you choose, something will survive. Life is hard to get going, but hard to get rid of. However, it would be fairly easy to wipe out humanity, and most of the other life on Earth, with the method as I've described.
The reason why countries fear nuclear war isn't just because they're afraid of being nuked. The fear is that, in one instant, enough nukes between two countries could be released to create an extinction event by the same process as how meteors and mega-volcanos cause extinction events. Not by a big explosion, but by choking out the sun and turning the Earth into an oven. Your country doesn't even have to be involved in the war, it could be on the other side of the world, and it'd get devastated, if not wiped out, all the same. There's enough firepower on the Earth right now, in terms of nuclear weapons, to cause an extinction event, numerous times over.
Depending on the countries involved, there is enough time for a targeted country to detect that they are under fire, determine that it will wipe them out, and launch all of their nukes back at the attacker in retaliation, thus ending the world.
Your little dose of terror for the day~