The major difference is the soldering as you mentioned.
The socket would allow you to replace the IC quickly - such sockets are used for testing of IC's for instance.
The soldered adapter could give lower contact resistance and maybe a bit less capacitance in total but I think it would not matter much.
I wonder though why you did not buy a HX711 readily assembled on a board with blocking capacitors and so on. For instance sparkfun offers a "SparkFun Load Cell Amplifier - HX711". There are a lot of modules around and you might find one where the pin headers are pre-soldered - so everything ready for breadboard.
Soldering of pin headers to such board might be a good starter to train soldering skills - it's not that magic really :)