I understand that the difference between 「見る」 and 「観る」 are similar to "look at" and "watch". That is, the first one is more like feeling and judging things by eyes, while the latter one is more like looking things with more attention. However, 「観る」 is not included in the list of daily used Kanji. That is, 「観る」 is not officially recognised to be read as "みる". So, it is safer to use 「見る」 if you do not know which one to be chosen.

You can use 観る(みる) to mean 'observe', 'go sightseeing', 'tell fortune', and 'see something from a distance'. 昆虫の生態を観る observe the ecology of insects 名所旧跡を観る visit famous and historical places 手相を観る read someone's hand 野球を観る watch a baseball game However, you can also use 見る instead in any of the cases above.

はい、分かりました。どうもありがとうございます　Akatuyさん。

これに限らず漢語で覚えれば問題なし。 観察、鑑賞、観劇。　見物、見学。　使い方の違いが分かりますか。

どうもありがとうございます　Asakoさん。