This is an interesting question. The short answer is that you need both.
First, it depends where it is. The ( Sablon King ) power cord feeding my Sound Application TT-7 power conditioner makes a much bigger difference than the LPS feeding one of my fiber media converters that is not directly in the streaming network path. On the other hand, the LPS feeding my DAC makes a much bigger difference than the power cord feeding my turntable.
But then things get more complex, because as you keep improving the power supplies in your system, your system becomes more transparent / resolving, and power cords make a bigger difference. I see them as two moving targets - depending on the time (i.e. the state of your system) and position of these moving targets, one can be better than the other.
Some common sense should apply, though. The LPS on the DAC matters a lot. A good LPS on my Chord DAVE DAC instead of the stock SMPS, even with a cheap cable, makes a bigger difference than an expensive power cord with the stock SMPS. I've tried a $16K power cord with the regular SMPS and a $6K LPS with a cheap power cord and prefered the LPS in this position. The power cord feeding your power conditioner that is feeding your entire system matters a lot (and impacts the entire system). The power cords to my amplifiers also make a big difference.
On the transparency comment - I talked to a power cable manufacturer this week and mentioned my TT-7 power conditioner and suggested to him to try one. His immediate reaction was: "$20K!!! Does it make good power cables unnecessary???". I think it was a serious question. I said: "Absolutely no! It makes power cords even more important, especially the one feeding the power conditioner". I told him if he is making power cords and wants demo the difference between power cords, the TT-7 is a must have tool for him!