This is something really new to me.- I won't say (that) one is better than the other. (future tense)
- I wouldn't say (that) one was better than the other. (subjunctive)
We often use the bold "would" phrases to mean "I think" or "My opinion is". I do think it is softer, since it points out "this is my opinion", not "this is a fact". We also use other phrases for that:I would say we will have good weather today.
I would guess she is about sixteen years old.
I would estimate there are a billion people in China.
I would say the Ethiopian won the race.
This is what I have learnt. Thank you sincerely for your explanation and clarification.As for your original question, your native speaker could say "is" or "was," and they're both correct and both roughly equivalent.
[L]inguists nowadays refer to the subjunctive in English with examples like "I suggest that you be careful" and "It is important that she stay by your side." (Wikipedia) or "I wish he were here right now (my own example).