Euclidean distance (norm of difference) and dot predict are [proportional to each other][1], so roughly the same:

> After normalizing $a$ and $b$ such that$\|a\| = 1$ and $\|b\| = 1$,
> these three measures are related as:  
> 
> Euclidean distance = $\| a - b \| = \sqrt{\| a \|^2 + \|b\|^2 - 2
 a^Tb} =\sqrt{2 - 2 \cos(\theta_{ab})}$  
> 
> Dot product = $\|a\|\|b\| \cos(\theta_{ab}) = 1 \cdot 1 \cdot
 \cos(\theta_{ab}) = \cos(\theta_{ab}) $  
> 
> Cosine = $\cos(\theta_{ab})$  
> 
> Thus, all three similarity measures are equivalent because they are
> proportional to $\cos(\theta_{ab})$.

 as [also discussed in here][2]. There was even an empirical evaluation by [Qian et al (2004)][3] concluding that 

> Through our theoretical analysis and experimental results, we conclude
> that EUD and CAD are similar when applied to high dimensional NN
> queries. For normalized data and clustered data, EUD and CAD becomes
> even more similar.


  [1]: https://developers.google.com/machine-learning/clustering/similarity/measuring-similarity
  [2]: https://skeptric.com/cosine-is-euclidean/
  [3]: https://www.cse.msu.edu/~pramanik/research/papers/2003Papers/sac04.pdf