In both dramas, the main similarity is the transformation of the FLs.
So, the FL in My ID is Gangnam Beauty gets a plastic surgery where as in True Beauty, she doesn't. Both dramas have a Love Triangle..

*SPOILER*
Another similarity is that the FL's best friend in both dramas turn into their enemy causing problems.
Well, another one is just that - even though, knowing the FL's actual face in Gangnam Beauty, he continues to like her and so as in True Beauty, well, similar but she does actually continues with her face without plastic surgery.

IMO, I prefer True Beauty...