If you nuke the NCR that screws Houses plans and NCR in general. If you nuke the Legion you screw Houses plans and the civillians and slaves of the Legion. Whatever you choose to nuke, you upset the balance. Get known as the guy who used nukes against a faction you will have an entire faction sending every assassin and rat toward you. You destroy the economy of vegas, render the victory at Hoover dam more or less redundant, because any part nuked will be to weak to hold it / attack it / defend it.

Sacrificing EDE is the lesser evil, the obvious choise, the paladin-esque cookie cutter act, ect. Its not thought through.

... I dont give a crap. I nuke the legion. That makes me look good to the NCR, saves them resources they can use on the strip where Mr House and myself will be waiting for them with open hands and black hole wallets. It'll make me and vegas look less like bastards when we rout them from the dam and make the NCR leadership look even more incompetent (they couldnt even handle a Legion which just suffered a nuclear attack... oy vey). Should the NCR cause the weakened Legion to have a total rout it will be a mighty surprise to them to have a securitron army ambushing them. And then if I am going to betray the legion, I might as well do it so thoroughly that they crumble completely, robbed of all leadership, infrastructure and military might (at least in the Mohave). EDE is a bonus.... one that I really don't use because I see him as ridiculously overpowered as a companion even before the upgrades.