It actually had 100 health I believe at one point since S3 and it's armor was changed to reducing basic attack damage. That's its true value. While yes, Doran's Blade can offer 1.7-2.9 health (Don't forget lifesteal is damage you do, not the base so you don't actually lifesteal 1.7-2,9 per auto), Doran's blocks 8 damage from both basic attacks and point-click spells. So, even using your math at the most extreme value that can't be quite achieved due to resistances of 2.9 (Don't take this as an insult, literally easiest way I could put it), it would take about 3 autos from a Dorans blade to make up for the damage blocked from one auto or point click spell alone by shield.
That's not including further life steal reduction cut by losing the 8 damage initially from Doran's blade in a 1v1. Basically, top lane match up, take your AD after Dorans blade, subtract 8 (Ironically cancel each other out almost) and then calculate the actual damage you deal to that champion post-resistance (Account for any other champion-specific reductions, i.e Fizz's passive) and you'll get your lifesteal. You'll find it's much smaller than 1.7-2.9. Then take that value and see how many autos you need to do to equal 8, as gaining back 8 health is the same as negating 8 damage. So, roughly 4-5 autos early on and you get the sustain from blocking one auto. This is, by the way, not even factoring in the base regen it gives you as well, although admittedly that's not heavily impactful. So, if you have the attack speed of full build old machine gun kog (5 attack speed), then it's completely worth it. Otherwise, on a serious note, it's never even early on.
Doran's blade scales better. Percentage lifesteal carries on as damage increases. It also helps your damage scale slightly in the beginning due to your abilities scaling off of AD, but the 8 AD scaling on abilities doesn't make up for the block, especially if any of those abilities are single target as the scaling is negated. But, that percentage is small at first, where base stats are strongest, so that's why Doran's shield is better very early game as it adds much more tankiness to you.
However, it's all game-by-game. Doran's shield start can easily be worse than Doran's blade if fighting an AP champ that doesn't rely on autos or single target spells. However Doran's shield kicks blade's ass in any match up that requires heavy autos. Otherwise, vs AD (As AD tends to use Autos whether they are AD casters or not), shield tends to be better early levels.
Now this doesn't mean you can counter anyone building blade with shield, countering is done in your actual mechanics and champion. But, statistically, unless I did the math wrong, Doran's shield should produce better results early game in terms of simply champion dueling. This doesn't account for CSing in general (Blade always better) or farming under tower, as well as shoving objectives.
Your claim about not being able to defeat people with Blade's makes me curious, because that's not something I see. I see it swing either way, however there is a potential explanation I have for your case, in that Doran's Blade can outperform shield in skirmishes and pokes. Shield is obviously, like a tank, designed to stand firm and fight directly. So taking someone like, say Fiora, can easily abuse the +8 damage it gives to Q/auto and skirt away, or even just Q, it's understandable to see how shield is losing here because it's taking damage, and although it's reducing it as intended, you're not returning damage as efficiently as a standing 1 on 1 so you're not able to "Out-sustain" your opponent.
Taking all this into consideration, really the only plausible conclusion we can draw is that it's heavily match-dependent. A nautilus with shield vs Fiora with blade and a nautilus with shield vs Tryndamere with blade are too heavily different match ups as Fiora can abuse the quick in-n-out pokes, while Trynd can't really poke, he has to walk up and auto (Could argue could walk up, auto and spin away, but it's not quite the same as Fiora). So while Doran's blade may work for Fiora (Or think any champion with AD poke Vayne, Jayce, Pantheon), it won't work so well vs shield as champs like Jax, Trynd, Trundle.
So finally, we look at the very last thing, as obviously my example with Nautilus was bias due to blade not being a real option for him. Take someone like Darius. Blade or shield. His kit screams damage, and he has an auto enhance, so you can quickly weave autos in for lifesteal as well as his passive encouraging more autos to stack. Logically, someone would take blade. And they really often do.
On the other hand, you could go shield, still keep a majority of your sustain (Talking just with his Q, not including the shield damage reduction/regen as a part of this), lose some overall damage across the board, but live longer which allows you to Q more often for sustain and more damage and have more time to stack your passive (Usually an auto win if you hit 5, unless about dead). Then, you get a massive AD steroid that makes 8 AD not so good. Logically, someone would take shield. And they really often do.
It's all situational in this game.
Aggressive? Go Blade. Poke? Go blade. Think you can one-way trade? Go blade. Want better cs/cs under tower easily? Go Blade. Want to scale a little harder with that item until you sell it late game? Go Blade.
Defensive? Go shield. Two way trade? Go shield. Stand and fight champions? Go shield. More sustain early game (Mathematically in most cases) vs champions? Go shield.
It's personal preference. One isn't strictly better than the other. I personally like Blade, as I love damage and am very aggressive in lane, plus I hate CSing under tower, or ever actually, so the 8 AD allows me to prep ranged minions with an auto and auto after tower shot and just auto after two shots for melee minions. When choosing, think of your lane opponent and how he will be doing damage to you. Fighting someone like Trynd? Shield is probably your best bet as he stands, fights and autos. Fighting someone like Poppy? Blade is your best bet as you probably don't stand a chance squaring up to her and a LOT of her damage isn't single target
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