You may be confused by some reports of material strength using its strain.
Because, theoretically, fibres in an undamaged laminate break at a given tensile strain in the fibre direction, for a long while quoting strengths by the amount of strain was common, and is still widely used. It is most applicable to carbon, and ignores contributions from the matrix. It is somewhat less true for compression failure, where kinking and microbuckling take place.
In this case doubling the proportion of fibres in a given direction will very roughly double the strength in that direction, so that strength in a given direction is more or less proportional to stiffness in that direction.
However, when damage is taken into account things get rather more complicated. In this case a lot will depend on the damage (probably impact or open hole) and the loading (tension, compression or shear or a mixture), but generally a laminate with double the stiffness in a given direction will not have double the strength; it will be less than double.
You must also be careful of the total fibre volume fraction (Fv); a laminate with 40% Fv will have a strength and stiffness significantly less than one with 60% Fv. For an undamaged laminate it may be roughly proportional to Fv, but again damage complicates matters.
I've addressed the effect of stiffness on strength, and your question was for strength on stiffness. However, the two effects are equivalent given my assumptions, and your second question is for stiffness-on-strength anyway. One answer is 'it might roughly halve it, in the absence of damage.' However, SW is right to be cautious. The real answer is 'it depends. We need more information.'
