There are far more similarities between these 2 televisions than differences. Both use the same LG OLED panel as LG has a near monopoly due to patents they own. Both are top of the line 4K HDR televisions.
Some differences do exist.
Design: A back panel exists on the Sony A1E which acts as a stand. As a consequence of this the screen of the Sony has a slight upward tilt which some may find annoying.
The LG C7 has a much more traditional stand which supports the TV quite well.
Input lag: The LG C7 has a lower input lag of 21 ms as compared to the input lag on the Sony A1E which is 31 ms.
Both displays can get very bright and are great for HDR content.
There is no motion blur on either panels since they are OLED.
Overall the LG C7 is a much better value.
I would consider both of these to display the best picture currently available.