Morphling vs. Lifestealer

Just the other day, I played a game as Morphling for our team's hard carry. We also had a KotL, Dazzle, Gyro, and QoP on our team, vs a Lifestealer, Leshrac, Windrunner, Venge, and Lone Druid on their team. The game ran for over an hour, and both me and Lifestealer were level 25 and extremely farmed by the end of it.

My question to you is, who would win that fight in a 1v1? I ask because my team won in the end, but I don't know if we really deserved to win because we made plenty of mistakes that should've cost us the game.

Anyway, of the two heroes mentioned, who is the harder carry? If you knew you were going to be facing off, would you build your core items differently? If so, how? Any comments appreciated. :)

Morphing is a harder carry hands down. He morphs all agility giving lifestealer little health to steal and the armor prevents physical damage. Plus, lifestealer doesnt have much armor unless he gets an AC. Replicant will also do alot of work. On morph, id go regular items. Linkins, eth blade, skadi, bfly and satanic.

You do realise Lifestealer will have a Abyssal Blade and Morphling will be dead in no time, right?

I agree, and also the magic immunity really won't hurt morph. If he gets slowed he can also reposition himself and get an advantage. If you have made some mistakes (that could/should have costed the game that doesn't matter since the enemy also did (and costed them the game)
You can easilly overpower the Lifestealer with your agility and your ult. If you manage to clear the wawe he won't be able to ult and since we're talking about a 1v1 his team won't be able to just ult in one of them.

And Morphling could have E-Blade, meaning LS wouldn't be able to do anything. It's a two way street, and there's a million different ways it could turn out. I hate when "1v1's are brought up because of this, especially with Abyssal Blade, Butterfly and Monkey King Bar. There's ways to bypass all of that, and there's ways to counter those proxies. Morphling can morph strength to survive while he is stunned, after that perhaps he has a Skadi so he could easily kite Lifestealer around.

Personally, I feel Morphling would win if they both had full items. Morphling is one of the hardest carries in the game because he can morph and get so much damage and armor, or morph while shut down and survive insane amounts of damage. Lifestealer is a pretty hard carry, but compared to other "hard carries" he won't win vs them late game, he excels mid game and early late game, since he is fairly easy to deal with if you have the right heroes/items.

Another thing, easily just as viable to get an Abyssal on Morphling in the theoretical situation. 10% chance to bash, sure, but it gives plenty of damage and the guaranteed stun that goes through magic immunity could be applied to Lifestealer.

Well, it's interesting that you guys mention some of those items, because Lifestealer did in fact build an Abyssal Blade. His problem was that I had built a Manta Style, so he only actually stunned me once, and my illusions the other few times we fought.

If you were interested in our complete builds, I had:
Power Treads
Manta Style
Eye of Skadi
Linken's Sphere
BKB
Aegis (most of the time)

Lifestealer had:
Power Treads
Hand of Midas
Desolator
Heart of Tarrasque
Abyssal Blade
Armlet of Mordiggian

I realize that my build may not have been the best, but eh. It kind of worked in the end.

Thanks for the great responses. :)