"I'm better at X than you are at Y" or "I love X more than I miss Y"

Question

Preface: If "I'm better at X than you are at Y" or "I love X more than I miss Y" don't use the same construct, please advise and I will edit this post to ask only one question or the other. I've included both under the assumption that they are related and thus may use a similar grammatical construction.

Question: When expressing two disjunctive ideas that may or may not be attributable to the same person and that are not of the same metric, what is the correct grammatical construct to use?

Examples of what I'm asking:

1) I'm better at playing basketball than John is at singing karaoke. (different parties (i.e., me versus you), different metrics (i.e., playing versus singing))

2) I love Japan more than I miss America (so I'll stay in Japan). (same party (i.e., me), different metrics (i.e., love versus miss))

Background: I've been unable to find such a construct in either A Dictionary of Advanced Japanese Grammar, A Dictionary of Intermediate Japanese Grammar, or on Google. For whatever reason, I'm reminded of the two possible ways of expressing "while" (ながら when referring to the same person and 間/間に when referring to two different parties). I imagine that there exists a concise way of expressing something similar in the case of my question.

My attempt at an answer:

1) I'm better at playing basketball than John is at singing karaoke.

ジョンがカラオケを歌うのより僕はバスケが得意です。/ジョンがカラオケを歌うのより僕はバスケをやるの方が得意です。

2) I love Japan more than I miss America.

(僕は)アメリカが恋しいより日本が好きです。/(僕は)アメリカが恋しいより日本の方が好きです。

Answer 1

I would probably say...

1. ジョンのカラオケより、僕のバスケのほうがうまい。
2. アメリカは恋しいけど、(それよりも)日本のほうが好きだ。
   or アメリカには帰りたいけど、それよりも日本にいたい(気持ちのほうが強い)。

cf.

「私の英語より君の日本語のほうがうまいから、日本語でしゃべろう。」
"You're better at speaking Japanese than I am at speaking English, so let's speak Japanese."

「私の英作文能力より君の日本語読解力のほうが上だから、日本語で書くよ。」
"You're better at reading Japanese than I am at writing English, so I'll write in Japanese."