The fundamental difference between the two timelines is the presence of time travel. The flash sideways doesn't have it. This theory is about where and how the timeline split.
First, I want to clear up a misconception many people seem to have about whether or not Jughead was the cause of the timeline split. I apologize if this is obvious to some of you, but I've seen this mistake being made in the forums and in some of the theories. Jughead CAN still be the cause of the timeline splitting. It's just NOT the point of divergence (the moment when one timeline split into two timelines).
One would expect the cause of the split and the point of divergence to be the same. But with time travel as a factor, one has to account for paradoxes. That means the point of divergence would have to occur at the earliest time when the Losties traveled to the past. This would be the adventure of Sawyer, Juliet, Miles, etc.
Since we saw the statue was intact in one of their flashes, we can ascertain that they traveled at least as far back as 1867. (But for all we know, it could've been centuries before that.) So the earliest point in time that we know about would be the flash that begins with Sawyer holding onto the rope after the well closed up.
To determine when the timeline diverged, we have to question whether or not the presence of the rope was significant enough to affect the flow of events. If so, that is our point of divergence. It's possible that some unsuspecting explorers found the rope and dug a well to find out where it leads. We just don't know yet. But if the time traveling rope isn't the point of divergence, then it was definitely Locke turning the wheel which occured only minutes after Sawyer's rope time traveled. We know that action played a significant role in the timeline. Locke's wheel turn is what caused Sawyer and company to jump to 1974 which resulted in Faraday's field trip to Ann Harbor where he came up with the idea of detonating a hydrogen bomb. Sawyer's presence in Dharma also allowed Jack and his crew to infiltrate Dharma and carry out Faraday's wacky plan.
So basically, the point of divergence had to occur long before the 1970s. With time travel as a factor, we have to trace back the earliest event that caused a change. That would be either Sawyer's rope or Locke's turning of the wheel. Unless we learn that Jacob and MIB did some time hopping of their own. But I'm not going to base a theory on information we simply don't have. That would be guessing, not theorizing.