Uh... which color? Bird's Opening is typically for white and Alekhine's Defense is typically for black. That's comparing two very different things. I don't love either opening choice, but I'll probably pick Alekhine's Defense if I have to choose. I say this one because it is a hypermodern opening and at least there are ideas to work from.
Bird's Opening just weakens the king right from the first move.
If you don't know what a hypermodern opening is, then here is a video of mine explaining just that.
Which opening do you prefer
1
Alekhine
2
Bird
Tell me in the comments