What is the significance of sensitivity list?
In this first case, you have a process with sensitivity to the clock and reset lines.
process (clk, rst)
if (reset = '1') then
...
else
...
end if;

This process like any other process will only update the variables and/or signals inside of it using the given logic every delta time unit in simulation when a member of its sensitivity list has an event. In this case, every time the clock has an event (or a change) or every time the reset has an event. The reset logic above will perform whatever is in the appropriate if/else section (if for active high resets, else for active low resets). Thus, when the clock or reset changes the appropriate if/else section of the logic is performed depending on the state of the reset signal.
process (clk)
if (reset = '1') then
...
else
...
end if;

So now, if we look at the case where the reset is not a member of the sensitivity list. You are correct in saying that this will no longer be sensitive to changes in the reset but the process is still going to execute the logic inside its block on every clock event, the clock is still in the sensitivity list. Even though your reset is not in the sensitivity list, when your reset has changed the process will realize it during the clock event and execute the reset logic thus, your first case where I assume you don't reset the count.