Basically we use ほうが　in comparative sentences along with より. ラーメンをたべるとき、めん(麺）は、やわらかいより、かたいほうが　好きです。 Eating ramen, I like hard noodles more than soft noodles. わたしより　かのじょのほうが　日本語が　じょうずです。 She speaks Japanese better than me. So what about ほうがsentences without より like your examples? 敏子ちゃんは仕事が早いほうだ。 If I have to translate this into English, Toshiko-chan relatively works quickly. If it's definite that she works quickly, the sentence would be 敏子ちゃんは仕事が早い or 敏子ちゃんは仕事がすごく早い. But, If it's not very sure whether she works quickly or not quickly, the sentence should be softened and would be 敏子ちゃんは仕事が早い’ほうだ'. How about this one. (わたしは）他人には絶対に負けたくないほうだ。 I relatively don't like to loose. This is about 'myself'. In this case, yes, I might not be very sure that I don't like to loose, compared to other people. But also there might be some feeling that I don't want to say it so directly, so in order to soften the sentence, I would add ほうだ. Another example of this case. わたしは、英語が上手なほうだ。（と思う） I can communicate with English speakers pretty well, but don't want to show off. I would say like above, I even might add と思う　at the end to make it sound softer. By the way, your second exmple should be 物事にあまりこだわらないほうだ。 My translation is, I'm relatively unconcerned with trivialities. Sorry for the redundant explanation. I hope this helps you!