How good creatures are in close combat depends almost entirely on their physical characteristics, in other words how fast, strong, tough and ferocious they are. Armour remains useful for warding off blows and shots but weaponry becomes a secondary consideration – the best gun in the galaxy won't help if your opponent is bashing your brains out with a rock!
In close combat both players' models fight. How many blows are struck and who strikes first are discussed below. The rules are written assuming that there is only a single close combat occurring in the turn, of course there may be several separate assaults being fought simultaneously in different parts of the battlefield. If this is the case the player whose turn it is can choose what order to fight the combats in.
Work your way down the Initiative scores in each separate combat until everyone has fought (assuming they haven't already been killed by a model in cover or with a higher Initiative). If both sides have models with the same Initiative, attacks are made simultaneously.
Models in or behind cover always fight first, regardless of Initiative — see Who Strikes First for the full rule.