I make comparison between my old Digicam Sony DSC-W130, Nexus 5, and Nexus 5 HDR+ Mode
First thing to note: HDR+ is definitely much better than auto mode, always use it when possible!
Overall, I'm satisfied with the Nexus 5 camera, but it didn't beat the Sony. Nexus 5 outperformed the Sony with near scenes (lamp, kitchen), while the Sony did better with far away scenes (grass, socket). The sony captured more detail, but the Nexus produces better photos when they contain gradients such as shadows or shiny surfaces. The sensor of the Nexus camera is inferior, but I guess it makes up by better prost processing. For complex scenery, the Sony is better, for simple indoor scenery, the Nexus is better.
I didn't test low-light conditions, but that's actually one of the Nexus' strengths and I'm pretty sure it will outperform my old camera there.
First photo: Sony DSC-W130, second photo: Nexus 5 auto mode, third photo: Nexus 5 HDR+ Mode