Even so versus all the same

[ROBINDESBOIS]

What is the difference between even so and all the same?

[Tyrn]

In It's all the same for me one cannot replace it with even so :)

[Rusty]

When they mean "despite anything to the contrary/in spite of that," they are synonymous terms.

Tyrn's example, in a subject complement role, isn't the adverbial phrase you're curious about. Therefore, it can't be replaced with the adverbial phrase 'even so.'

Other adverbs and adverbial phrases can be substituted for 'all the same' and 'even so,' when they mean the same thing:
nevertheless, still, yet, despite that, in spite of (that), however, nonetheless, notwithstanding (that), be that as it may, though, just the same

Here's a page (https://www.collinsdictionary.com/dictionary/english-thesaurus/even-so) that gives examples. Here are a few more I found elsewhere:
Granted that it is dangerous, ...
all the same ...
even so ...
nonetheless/nevertheless ...
yet ...
I'd still like to go.

She wasn't very fond of dogs.
Still, ...
Yet, ...
However, ...
Even so, ...
All the same, ...
Nevertheless/Nonetheless, ...
Notwithstanding, ...
she let her roommate get one.
(https://www.merriam-webster.com/thesaurus/all%20the%20same and https://www.merriam-webster.com/thesaurus/even%20so)