Why models of stochastic gene expression predict that intrinsic noise should increase as the amount of transcript decrease
Reading Kaufmann and van Oudenaarden (2007), it seems to validate the first alternative (using results from the Central Limit Theorem):


  Although biochemical fluctuations influence all stages of gene expression, those involving molecules in extremely low abundance are expected from a statistical standpoint to be larger in magnitude and therefore to contribute disproportionately to the overall variation between cells.



Kaufmann, B. B. &amp; van Oudenaarden, A. Stochastic gene expression: from single molecules to the proteome. Curr. Opin. Genet. Dev. 17, 107–112 (2007).