Lux can get an amazing feed in her lane, lots of CS and still have a fail 5v5 teamfight presence.

You are ALWAYS going to feel the effects of a fed Morgana.

Gold for gold, Morgana contributes more.

Lux is better at support, morg is better at carry the team. I wouldnt mind if i have both on my team, but ill pick morg, cuz her ult is MUCH MORE DEVASTATING than lux's, even if the last beam hits only 1 enemy, it already did a better job than fulkeln with higher damage and a stun (2 times damage counted), plus i think morg Q has a better radius, i feel comfortable firing her bind than lux, cuz it deals sexy damage and longest snare

Morgana wins hands down. AOE Slow and Stun with shield that makes you immune to CC GG

They require rather different playstyles, and despite the similarities, they fit different roles.
Lux is a skirmisher, and does very well if she hangs around the back of a fight. Her range means that she's one of the few champions who can afford to build no defensive stats. She also ensures that nobody escapes with low health most of the time, which Morgana can't do.
Morgana can get in the middle of the action and deal a lot more damage total. Lux's relatively low AP scaling and very poor mana regen means that she's not likely to win a straight fight. Morgana will just stay there and let you beat on her while she saps your life and ends up killing you. Lux has a kit that lets her run away while still wearing you down.

The poll was misleading. I voted for Lux under the premise that I'd get to pick Morgana for myself.
While not as strong a 5v5 presence as Morg, Lux, I'd say, can make more kills. I build Morg as a tanky support; more of an initiator. She makes any engagement complete hell, but everything will be on cooldown after this, while a teammate cleans up. So while I'll have a low killscore as Morg, my assists are phenomenal; usually the highest in every game.

Lux I can't say much for; never played her. I'm more scared of her. I'll be blue pill in some bushes and she'll give me a boom, headshot from nowhere. Morg is a more intimate fighter, as you can imagine. Unless she's throwing some sneaky snare from across a wall (which can be hard to land) you will always know when Morgana is coming after you. Some say she has a conflicting tool kit but I see it as, "play defensively until you have built defensively."

I actually don't think this is going to be the end of Morgana's balance adjustments. It's highly possible they might tone her down further even after the Xerath patch.

Lux has a Laser. that's all

Morgana's a bit more difficult to play, and NOT a burst caster, but I'd rather have her impressive utility over Lux' any day. Morganas Snare is longer (if more difficult to land) her shield is far more useful, and her ult is an amazing ability for teamfighting.

black shield is sexy

It depends, both are good to my eyes. However if it's your way to pick a champion to buy, it really depends on what you want to do, despite looking similar in design, they are different in playstyle.

In my opinion Morgana in a duo lane is an ABERRATION. There, I said it. Morgana is the only champion I absolutely refuse to play if I do not get a solo lane. Reasons for that:

1) Your farm AND sustain push the lane, your lane partner will probably not be ok with that
2) Your farm relies on a DoT, if you're laning with a partner, especially if he's a carry, he IS going to steal all of them in your face
3) Morgana is EXTREMELY item dependant. She is one of the very few characters who suffered from the Zhonya split a bit less than a year ago, because she needed both tons of AP (now Deathcap) and the active (now Zhonya's Hourglass). You will need these two items in order to be effective. I also advice a RoA for mana and tankiness. These are very expensive items that you won't get in time in a duo lane. Without them Morgana is a snare bot whose shield can barely block one ability. I die inside when the enemy Morgana builds support.

Lux, on the other hand, does well in a duo lane (better than Morgana that's for sure), and is also a good solo. She's more mobile than Morgana, usually builds lots of CDR so her playstyle is more "active". Her E is a nice scouting tool, and her ultimate is very good to steal dragon/buffs and get a kill on a running *******.

It's really down to your playstyle. Want someone tankier with good sustain to solo a lane? Morgana. Wants a good poker who deals damage from afar and you don't know if you're going solo or duo? Lux.

As far as difficulties go, I find Morgana a bit harder to play, because her snare projectile is slower, and also the fact that she has to commit to a fight much more than Lux in order to do her job.