Euclidean distance vs. search space size

Calculating the euclidean distance between 2 vectors yields different results when querying different indices. I have 2 separate indices, one with 200,000+ embeddings and another with 5 embeddings. When I query both indices with the same embedding the euclidean distance with the top match (which returns an identical embedding among both indices) is different. The distance returned from the smaller index matches the distance I calculate locally (this is not the case with the larger index). Can I get confirmation that as the search space increases the euclidean distance will change? If this is the case would any of the other metrics (cosine similarity or dot product) alleviate this issue?