Barbell has high convexity than laddered portfolio. So does it mean that when the yield curve is changing, barbell provides higher protection than laddered or no?
Depends on twist and shifts of YC.
As Mr E says it depends on the twist / shift etc. There you will have to examine which is more susceptible mostly to the long end of the curve.
If there is a large parallel shift in the yield curve (all move up or down at the same level) then yes a barbell will be better than a laddered due to higher convexity. This is because of the equation for the price change in the yields (-MD x Change Yield) + (0.5 x convexity x yield squared). As the second part takes into account convexity is an addition it means that for a downward shift it yields the barbell will outperform the laddered and in an upward shift in yields it wont do as as bad as a laddered and hence outperform.