On tanks: Aside from the logistical problems, their main gun is not designed to kill the dead. What kills a man when not hit directly is the impact of the explosion, that is to say: preasure(Spelling?). The sudden shock of the explosion shuts down the organs in the core, as the body can't take the sudden change. It also makes the brain bounce around some, compress, but unless there is actual physical damage the zombie will survive.*
On mines of any sort: Mines are not designed to kill. Mines blow off a leg or two, they maim and cripple. The proper function of a mine is to send a countries soldiers home broken and useless. They now take hours and dollars of care by the state and their families. Enough amputies come back from a war, and a country loses the will to fight that war. Zombies do not have this problem. They loos a leg, or two, or their entire body except for arms and shoulders, and they'll still come after you. I would argue that they are in fact more dangerous when they crawl, as they are harder to see and more likely to sneak up on you if you're out of cover.
On fire, again...: A torch applied to the ligiments of a reanimated corpse would prove effective in a timely fashion. However, concentrated heat on all parts of a zombies body is unrealistic. It will take time. If time is not a problem, then yes, you can burn zombies to 'death.' However, if time is not a problem, I would argue that the fuel used to power your giant flamethrowers would see better use. Fueling generators, vehicles, for cooking, et cetera.
Fancy weapons sound like a lot of fun but can be difficult and dangerous and, above all, difficult to find. If you're own your own (not ideal, but in the zombocalypse, what is?) there are going to be a thousand things to be doing before you even consider reclaiming the world from the dead. If you're with a group, there will only be a few hundred other problems. I'd move that modern firearms, rifles specifically, would be the the most efficient weapon. However, it is unlikely one would be taking on an entire cities worth of a zombie horde without a fair number of mates, well trained, with a ridiculous sum of amunition.
~Sean
*I take this from World War Z, and my own rememberings when I used to be interested in modern weapons.
Edit: Damnit, Churchwarden, this is a serious issue! Zombies!