You asked this question whats-the-difference-between-the-听到-听见
And now you are asking the difference between 遇到 and 遇见
Let me explain [V + 到] and [v+ 见]for you here. 到 and 见 are result complement (read it and come back)
From that site, you see 到 indicates the action is successful, while 见 indicates the result of the action is 'see'
看 means 'to look' but doesn't include the result 'to see'
看见 = look (and actually see)
看到 = (successfully)look (= actually seen)
到 is a broadly used result complement, most verbs work with 到 because most verbs can have a successful result
见 as a result complement is very specific, it indicates the result of the verb is 'see' or 'detect'
Example:
看见 (look and see)
遇见 (encounter and see)
听见 (hear and detect)
You can replace 见 with 到 in all three examples above
Example:
看到 (successfully see = look and seen)
遇到 (successfully encounter = actually encountered)
听到 (successfully hear = actually heard)
We only use 见 when the result of the action is 'see; detect' and there are not many verb results in 'see', beside the three examples listed so far, I can only come up with
望见 - observe (and see)
夢见 - dream (and see)
碰见/ 撞见 - run into (and see)
闻见 - smell (and detect) - Cantonese)