Hi,
the problem is with the simulation of the AD8034 opamp. With my LTSpice version (latest), none of your circuits give a proper output for this opamp.
If your replace it with the LT1721 comparator for instance, it works fine.
Another way of making this simulation work is to power the AD8034 with a dual supply (+/-5V for instance) instead of single, or offset the input signal so that it nevers goes negative.
Why? There is an issue with your design which explains the simulation problem.
Your sine input signal is symmetrical (+/-1V peak-to-peak), whereas your opamp-based comparator is powered with a single supply. When the input signal goes below ground, past the Vf of the input clamp diode of the opamp (around -0.6V most likely), this diode will conduct and that's not good at all. You may end-up destroying your opamp and/or the stage which is driving the positive input if it can provide enough current.
In simulation, the spice model of the AD8034 doesn't seem to like that very much, whereas the LT1721's doesn't mind. Anyway, you have to consider using an input signal that doesn't get below ground, either by design or by shifting it, or use a dual supply. Another cheap solution if you can't afford that is to add a series resistor just before the positive input of the opamp (which btw is suggested in the AD8034 datasheet: "If the inputs are driven well beyond the rails, series input resistance should be included to limit the input bias current to <10 mA.")
In your simulation circuit, adding a 1k resistor between the sine source voltage and the positive input of the opamp is enough to make the simulation work, and most importantly, make it safe in real life.
NB: The AD8034 model in LTSpice seems definitely "temperamental" when on a single supply. On some runs, it worked properly with the series resistor, and on others, it would get stuck. The AD8031 works properly (and many others). Not sure if this is a problem with the model itself or with LTSpice, or a combination of both. From experience, I can just tell you that some spice models of opamps don't behave properly on single supplies even if the opamp itself is designed for it.