I am trying to find a word for it different than "arguably better" because I am trying to avoid arguing or pointing out the reasons why it is arguably.
May you suggest me an alternative word?
To start with, I believe you mean "arguably better" (in case you have to fall back on that phrase).
It depends a bit on the context, but perhaps you could use "recommended"? As in, instead of "That book is arguably better than the required textbook," you could say "That book is more highly recommended than the required textbook." Or, if you don't need to compare X to Y, you could use "That book is recommended."
You could replace
"This book is arguably better than the required textbook."
"I favour this book over the required textbook."
The use of "arguably" indicates that some people may disagree with your judgement. In the second sentence it is clear that you indicate your own preference and presumably your choice is rational!
If you want to avoid making absolute statements, as using "arguably" lets you do, this construction may work:
"This book may well be the better one of the two" or "This book may well be the best he's ever written".