ED-E, he has a better back story and so far hasn't died yet.

On my first play through I always chose Ed-e. The fire power, the ranged fighting, the flying robot that everyone comments on, was awesome, and I totally ignored Rex. But then on the third ending I always felt that I was too safe, Ed-e or another companion would always take them out before I could even upholster my weapon. I never got to complete any challenges because they took them all.

So this time I chose both Veronica and Rex, and I discovered two things. First, with both companions being melee, the time their charge gives me to upholster, aim, and unload. Second, their charging then distracts enemies, allowing me to shoot them in the mean time or maybe they can soften up hard enemies enough to let me kill enemies to still count for challenges.

Neither.
Either a battle bot with an annoying theme song or a robodog whos... A dog... Another... [censored]... Dog.... Can't there be a Fallout game that "isn't" trying to cling on to A Boy And His Dog for all it's worth?

I used ED-E. Bonus perception is really useful, and his FotA upgraded laser cannon is craaaaazy powerful.
Also, I pronounce his name "Eddie" is that right?

I was very nearly done with the game and never had the opportunity to have Ed-E as a companion. =[

Rex was okay, I suppose. Sure, it was bothersome to have him draw attention to us by always chasing after every enemy in sight and consequently dying all the time. He also got lost at one point and I had to make it all the way to Jacobstown before he finally showed up again. But it was certainly better to have him as a companion rather than being stuck on my own.

Personally, my favorite companion so far, is Veronica Santangelo. I have no idea how she does it, but her melee skills are unreal! lol

I thought I was the only one. It's VERY annoying! I even considered switching to Rex just to avoid hearing the noise. But ED-E's attack and perk are very, very good imo.

Each is handy in its own way. Rex will deftly clear out any of those annoying mantises, mole ratties, or Freeside thugs without you even having to lift a finger, and his upgrades make him pretty powerful (despite my disdain for Caesar and his queer slaving crucifixion-fetishists, I especially like the extra durability you get from "Blood of the Legion").

On the other hand, ED-E has a distance attack, and it will generally stay close to you in combat, allowing you to back it up. Rex often dashes into harm's way, and can easily die before I can get there to help. And I wouldn't want to do "Come Fly With Me" with anyone other than ED-E. His perk makes nightkin visible to you, Even if you choose to go with Rex, I'd consider switching to ED-E for this quest.

The only thing i like about ED-E is the increased compass range. He misses 90% of all his shots, he plays that crappy music and is constanly in the way! D:
Rex might die a lot but he takes his enemies with him

Rex is too much micromanagement for me, always have to look behind me to check whether he's still with me or run away somewhere to die. ED-E is immune to cazador poison and I always know that if I don't see anything on a radar is because there is no one.

Like Rex more, however use ED-E more.

The two are just to staged out from each other.
Then ED-E has a ranged weapon, and a better perk.

Rex however has far less bugs.

If I did not roleplay more and not care about perfect perks.. etc I'd just use ED-E.
As it is it's a split.