having an ele and necro to completion, big differences, few examples quick and dirty
want to be a minion mancer? necro only
soul reaping is key (death cycle - energy), pumping DM is key (max lvl minions).
An ele could never be close to the minion mancer a necro can
soul reap doesnt have skills, but the ability to gain energy as mobs fall is a nice bonus, crucial for MM
want to use the big time nukes/'echo' nuker? elementalist only
maxing out the key element and handling the exhaustion you need the mana pool. A necro simply couldn't handle the exhaust nor bring as much noise to the party. You could have a 'glyph renewal - meteor storm' necro say to mimic, but won't have the energy pool w/o energy storage, and will additionally exhaust out.
Can they work together though? Certainly.
But just like many other choices those runes on the armor (and the +1 'hat' of choice) and the primary attribute line has some important reprocussions.
Examples of working together-
E/N using Necro Elite Virulence, simply toss a condition spell (ie blinding flash) and followup with a whole lot of [armor avoiding] degen damage amongst your DD spells
N/E using Ele Elite Glyph of Renewal, use your favorite skill repeatedly and its not an enchantment and no points cost in an attribute line, Elite Glyph of Energy similiarly knocks the big minions costs (25e two of them) down a lot.
These are quick examples and certainly you dont need to grab the alternate elite to make it useful - you may want it from your primary

Take a look at the options, and realize you're capped at 12 for any secondary line (and that will cost a lot of attribute points), meanwhile your primary gets minor runes for every line (+1), a hat (+1) and one superior (+3) for one line is common.