Yes, we are ultimately stuck with a subjective appreciation and choice.
But that is true about anything important. There is no logic to prove that love is better than hate, beauty better than ugliness, melody better than noise, justice better than chaos, thanksgiving better than ingratitude. And God refuses to be proved. We love Him or reject him, and that is a free choice in which logic has no place whatever.
I am not sure what kind of Buddhism you are in touch with. I lived in Varanasi within two or three kilometres of the stupa that marks where Buddha preached his first sermon. Buddha's original message was that we are all bothered with desires, so if we could get rid of all our desires that would be -nirvana-. That used to be the object of going into a Theravada monastery to eradicate our desires like weeds from a garden. But to me all that I value as a person requires desires (love, joy, music, art, food, family), so losing all my desires would be the termination of myself as a person. But if someone wants that, then Theravada Buddhism is far better than what Christian faith has to offer. Mahayana Buddhism is quite different, and Zen Buddhism something else again. In each case there are implications to the choice we make, but there is no logic to prove that the choice is logically correct and other alternatives are wrong.
If you wanted to pursue this carefully, you might work through God
of Many Names on my web site.