First, 3) above isn't so -- if you plot the same data with plot() and with errorbar() the two lines will overlap identically; the problem in that figure is you're comparing 2) to 1) -- plot() and friends draw straight lines between the plotted points; if there's sufficient curvature between the points as in your examples above, then when overlay with more points, then the difference does show up.
To do what you want wasn't foreseen by TMW with a builtin option so you'll have to do it yourself but it's not difficult...from an example for errorbar()...
x = linspace(0,2,1000);
y = exp(x);
err = zeros(size(y));
N=100;
ixErr=1:N:numel(y);
err(ixErr) = 0.3*y(ixErr);
hEB=errorbar(x,y,err);
Adjust N as wished to pick as many as you wish...oh. Forgotted about 'CapSize' -- it still draws the vertical line caps for all the points even though the error value is zero--bummer.
In that case, it's probably simpler to not draw the line for errorbar but only with the original plot().
figure
hL=plot(x,y,'b-');
hold on
hEB=errorbar(x(ixErr),y(ixErr),err(ixErr),'b');
You may have to create a fake errorbar with no actual data that uses the line style and color you want the legend to be to avoid the previous artifact of different line segments between the actual and errorbar.
Dealing with this more cleanly would seem a worthwhile enhancement request for errorbar.
