A very good upgrade in more ways than one to a card that's normally used for its high soak.
The first change we see is that you can now use this ability on ANY investigator rather than just yourself, which includes not having to be at their location. Just like Ward of Protection (2) this means you can always be ready to counter the Ancient Evils that the Guardian at the other side of the map drew.
Now for the real boost. The lv 0 version allowed you to draw a card, say "yikes!", shuffle it into the encounter deck, draw another card, and if you were unlucky say "even more yikes!" and wish you hadn't used the ability. And to make things worse you're simply postponing the danger as the first card is still in the encounter deck.
This card, however, gives you the choice between the two so you will ALWAYS negate the "even more yikes!" encounter card. Either you negate the first card that was bad enough for you to use this ability, or you negate the second card which would have been even worse. Dr. Billy T-M never misses! Additionally, the lv 2 card actually "cancels and discards" the card you choose. You don't shuffle the lit fuse into the encounter deck like before, it simply discards.
So not only does it supercharge the original ability, it also allows it to be used on the rest of the map. The downside compared to similar cards like Forewarned is of course that you (or your ally) must still resolve the lesser of the two evils. But this is a fair price to pay for an ability that can be triggered every mythos phase.
But why would you choose Billy over other cards that doesn't take a hotly contested ally slot like the previously mentioned Ward of Protection, Forewarned, and A Test of Will? The reason is that Billy doesn't care about your revelation effects. Billy doesn't care that there's a "Surge" written above "Revelation". Billy doesn't care that enemies aren't revelation effects. Billy sees a card he doesn't like and cancels it.
As for the cost, placing a clue down, it's not all downsides. Crack the Case, Hawk-Eye Folding Camera, and cards that only work while standing on clues like Inquiring Mind and Preposterous Sketches are easier to trigger. Not to mention Research Notes from the same expansion.
Incredible encounter deck manipulation. Billy has indeed been "Working on Something Bigger".