I currently run a deck for Standard, Modern, Commander and Legacy. For standard, I have a typical, horribly budget Rakdos Deck Wins. For Modern, I have a very lovable mono-green, resistant to removal type of deck. For Legacy, I'm trying too hard to break Pyromancer Ascension . For Commander/EDH, I'm running The Mimeoplasm . A little morals thing about me, I like winning through combos, but not infinitely.
However quiet, I am a Christian, so feel free to tell me you are too, it's always a relief.
First strike damage will happen before regular damage, so the little guy will deal deathtouch damage first. The other creature will die before it gets a chance to deal any damage to the smaller creature, so the smaller creature will live.