From the textual inversion guy's own comment on Twitter

>The objective is similar, but it's: (1) A different approach - they also fine tune the model itself, and they get much much better identity preservation!

dreambooth retains higher fidelity as the model is finetuned, but to be honest I think textual inversion is actually more applicable as you can just add some embeddings to inject new knowledge into the model and not an whole new model just for a single concept (if you want to share it with others). Also I have not seen dreambooth being applied to replicate styles.