This is an age old debate that has been discussed a great deal already by various gamers. There are those who prefer to min max and create a crack monkey attacking soldier type with a set of tricks to make NPC's die quickly and move on to the next fight. And then there are the people who craft a story and character, a voice and personality, and who care less about the mechanics and more for the fun of playing their character. And yes some even blend the two or are capable of shining both in combat and when talking in character is called for.
It boils down to preference and what is most fun for the player, since everyone is different. If you know how to make a Druid/Monk who can Wildshape into an Air Elemental to get that AC of 37, and then throw the badguys around the map, go for it, have fun making the GM complain how none of his NPC's can hit your PC. And if you prefer a twisted background that might not be optimal but will be a pleasure to roleplay out, then more power to you as well.
Personally I prefer to have a great character that I'll enjoy playing. I tend to try to make them great at their role via the mechanics, but I usually shy away from optimizing most of the time. Mechanics and the numbers, feats n gear can only take you so far. Building a personality, a story and breathing life into the character is more my style of gaming. But I am not going to reject another persons preference to have his min-maxed Tiefling Barbarian either. To each their own.