I think one has to analyse a person's exact state of mind who fears their eventual demise. Rationality I take in the sense of instrumental rationality - taking efficient means to clearly conceived ends. I also assume that 1) is a pill which which, if taken, would be known by me - or justifiably believed - to render me immortal. Likewise, the properties of pill 2) are known or justifiably believed by me. Else their properties wouldn't be relevant to my practical reasoning. I put myself forward as the chooser.
If I am plagued with fear, is it the fear of death that I want to be free from? In that case there is no rational preference between 1) and 2) : both accomplish the removal of my fear of death.
Or is it the eventual demise that I fear ? If so, 1) is the rationally preferable choice since 2) does nothing to prevent the eventuality I fear, namely death; it simply removes my fear of it.
Take a parallel with terminal cancer. Is it the fear of terminal cancer from which I want to be free ? Or is it terminal cancer. 1) A pill that removed all possibility of cancer and was known by me to do so, and 2) a pill that just removed my fear, would be rationally equivalent. If in contrast it's the terminal cancer I fear, 1) is rationally preferable.