Noncovalent polymer-single walled carbon nanotube (SWCNT) conjugates have gained recent interest due to their prevalent use as electrochemical and optical sensors, SWCNT-based therapeutics, and for SWCNT separation. However, little is known about the effects of polymer-SWCNT molecular interactions on functional properties of these conjugates. In this work, we show that SWCNT complexed with related polynucleotide polymers (DNA, RNA) have dramatically different fluorescence stability. Surprisingly, we find a difference of nearly 2500-fold in fluorescence emission between the most fluorescently stable DNA-SWCNT complex, C₃₀ DNA-SWCNT, compared to the least fluorescently stable complex, (AT)₇A-(GU)₇G DNA-RNA hybrid-SWCNT. We further reveal the existence of three regimes in which SWCNT fluorescence varies nonmonotonically with SWCNT concentration. We utilize molecular dynamics simulations to elucidate the conformation and atomic details of SWCNT-corona phase interactions. Our results show that variations in polynucleotide sequence or sugar backbone can lead to large changes in the conformational stability of the polymer SWCNT corona and the SWCNT optical response. Finally, we demonstrate the effect of the coronae on the response of a recently developed dopamine nanosensor, based on (GT)₁₅ DNA- and (GU)₁₅ RNA-SWCNT complexes. Our results clarify several features of the sequence dependence of corona phases produced by polynucleotides adsorbed to single walled carbon nanotubes, and the implications for molecular recognition in such phases.