The first image is magnificent....those eyes really make the shot ! The selective DOF on the face is well done.
No. 2, I feel, is let down by not enough DOF. The nose is "just" OOF , leaving the hair on the bridge of the nose in focus. IMO, it would have been a better image if the nose/nostril had been in focus.
Although the high ISO looks quite bad on-screen, printed out, the image shouldn't look too bad.
I guess it comes down to what the image is intended for (if anything).
But as steffen said, "a good shot is a good shot"....and it's better to get that shot (with noise) than not have that shot at all.
PS..what lens were you using ?