Any wise Christian knows they're not perfect. You can study Scripture day in and day out, you will inevitably fail to understand something, because while God and His word are perfect, man and his thoughts are not. We have biases, preconceptions, frailties, and many other things that make it very difficult to be right on everything. Thus, while I obviously don't know what they all are, I know I have errors in my worldview.
If I could choose what one of them was, I would immediately default to Eternal Torment. I hate the idea of Hell, I hate that it lasts forever, and so if I could be convinced by some variant of Annihilationism, I would jump on that in a heartbeat. On both a personal level, and with regard to apologetics, it would just make things so much better for me.
The primary reason for that is that it is an objectively nicer doctrine. Thus, for us as Christians, it is far more comforting, and of course it removes an obstacle for many non-Christians, who see Hell as overkill (no pun intended) on God's part. Many Annihilationists even argue this way. We should be Annihilationists, they say, because Eternal Torment is inconsistent with God's character, and offputting to unbelievers.
But this rather tips their hand, admitting that they have motive. This doesn't necessarily disprove their view, of course. You can be as biased towards the truth as against it. But when you substitute motive for argument, it weakens your case. Thus, these same Annihilationists will often argue that actually, it's worse to just stop existing than to suffer in Hell forever.
Now, ultimately, this part of the argument will often come down to personal preference. We all have different fears, desires, and opinions. Thus, we see disparate results in every game of "Would You Rather?". Would you rather stop existing, or suffer in Hell forever? Different people are going to give different answers. For me, it's an easy choice. I've suffered Earthly pains I'd rather cease to exist than endure forever, so if faced with the choice between receiving the due penalty for my sins either forever, or temporarily, I'd opt to turn out the lights.
But the opinions of the omniscient God will always hold greater weight. If God says "it's better this way", it is better this way. And as it happens, Scripture does weigh in on whether it is better to live and suffer than not to exist.
To begin with, let's give a purely human example. Take Job. One of his many laments was to curse the day he was born, and quite loquaciously. 24 verses of the 3rd chapter of Job are dedicated to it.
But one might ask, even with Job being inspired Scripture, why this matters? After all, Satan's words are recorded in Scripture, too, but we can't exactly trust his conclusions. And so we can afford to let Job be a man in both grief and error. We cannot, however, apply this logic to Jesus.
So, what are Jesus' opinions on this matter? Of course, since no one flat out asked Him "hey Jesus, is it better not to exist, or to suffer in Hell forever?" Thus, we have no explicit answer. However, His strong words against Judas don't leave much to the imagination. In Matthew 26:24 and Mark 14:21, Jesus makes a reference to the fate of His betrayer, both times saying "...woe to that man by whom the Son of Man is betrayed! It would have been good for that man if he had not been born."
As it stands, Judas exists. He is a real man, brought forth from his mother's womb on the day appointed by the Lord, as all of us. He was capable of sin, and receiving the consequences thereof. These consequences, whatever they are, are worse than if he was never born.
Now, it is possible to argue that "never born" may not be exactly equivalent to never existing. After all, even in his lament, Job speaks as much about dying as an infant as about simply never being conceived. And Jesus certainly knows the fate of children who die. But given that this fate appears to be eternal bliss, it is simply a given that any fate will be worse than that. Thus, it does seem "never born", in this case, means never existing.
Now, if Judas' ultimate fate is to eventually cease to exist, never perceiving that he even did, his fate is not worse than, but identical to if he was never born. There is just no realistic way around this. Therefore, Jesus' words not only weigh in on whether it is better to stop existing or suffer forever, but also suggest that Judas will suffer forever.
In my eyes, it would be fantastic if I was wrong on this. If Judas will be raised mortal again, only to burn away in due time, along with all the impenitent, I will be a happy man. But I don't see, given this statement, how that is possible.