The best way to think about the difference between these two is that Eldritch Scoundrel is a Rogue who has Wizard abilities, while an Arcane Trickster is a Wizard who has Rogue abilities.
Eldritch Scoundrel works best with two-handed finessable weapons like the Estoc, Elven Curve Blade, or Elven Branched Spear. Because you need a free hand to cast spells you can't dual-wield, but two-handed weapons work just fine. By utilizing the Vanishing Trick ninja trick (which you can use by sacrificing a 1st level spell) you can have swift action invisibility available, creating for a really nice tricky rogue attacker. I really like the Eldritch Scoundrel, but the one thing I'd caution is that it's really slow to get rolling and at 1st and 2nd level it feels like a weak Wizard.
Arcane Trickster is a Wizard first. By using the Accomplished Sneak Attacker feat you can qualify with only 1 level of Rogue, maximizing your Wizard levels. You can then focus your character around delivering sneak attacks with ray spells. This approach generally doesn't do well with weapons, and if you do want to go the melee combat route then you'll want to focus on the polymorph spells and use natural attacks and not daggers.