In fact, the different of Line out and headphone out is depend on the load,
Headphone out is design to drive some low impedance loader, and Line out is design to drive some high impedance loader. a good headphone out may be far more better than a bad line out.
Even double amp could have better sound quality , of course, all depend on science. for example
There are one DAP call A, which have headphone out and line out, and the distortion of the HP is 0.01% at 10k loader and 0.1 at 32 ohms, this is the common result of a amp ( not matter it is line amplifier or power ampliifer ), and the line out is 0.001% at 10k loader
There are one headphone amp call B, which input impedance is 10k, and the distortion is 0.01 % from power out at 32 ohms.
the distortion of A is 0.1% from headphone out.
the distortion of A+B by connect the HO to B, will be closed to 0.02%.
the distortion of A+B by connect the LO to B, will be closed to 0.015%
So, the best will be use line out to connect a audio source to amp, but you still get better SQ by connect a amp to a audio source by headphone out.