Do the Japanese read Classical Chinese poems in Japanese or in on-readings?

Question

The pros and cons of both approaches are obvious.

1) If you read by conversion into Japanese through kanbun, you get the sense. Meanwhile, you lose the rhythm, and sometimes it is not obvious what the Japanese rendering is.

2) If you read by string of on-readings, there is rhythm, and it rhymes! But any hope that it is understandable to the bystanders is excluded.

How do Japanese normally do?

Answer 1

There is always trade-off, as you said. Thus naturally we have both approaches, depending on what policy and objective you have.

Your #1 is called 訓読 ("interpretative reading") in Japanese, and considered normal. As it is a form of literal translation, you can relatively easily get the meaning, at the cost of original prosody. Fortunately, Japanese verse does not count foot, just meter, so it is not impossible to make up a "rhyming" translation with a little contrived idea. (訓読 has a much fixed set of rules on how to translate the grammar, but has no restriction on which word you choose for a character.) There are works such as 和漢朗詠集, which collects "musical" Chinese poems when read in Japanese. We also have idioms originated from 訓読 and have incorporated into ordinary Japanese. Many people are only familiar with 訓読 as today's Classical Chinese curriculum only deals with it.

On the other hand, #2 is called 直読 ("direct reading"). It retains the original rhythm and prosody, as long as you can read it in correct pronunciation, and a fair amount of it even in the current form of on'yomi. This method is traditionally applied to pedagogical scene, and not the usual way to enjoy works except for those who has mastered the Chinese grammar or interested in the original rhythm.

There is another special practice called 文選【もんぜん】読み, which pronounces the on'yomi first, then Japanese reading second. This is also a classroom methodology. The most typical example is its use in reciting of 千字文 (cited from this article).

テンチのあめつちは
　　　ゲンコウとくろく・きなり（天地玄黄）
ウチュウのおおぞらは
　　　コウコウとおおいに・おおきなり（宇宙洪荒）
ジツゲツのひ・つきは
　　　エイショクとみち・かく（日月盈昃）
シンシュクのほしのやどりは
　　　レッチョウとつらなり・はる（辰宿列張）
カンライとさむきこときたれば
　　　ショオウとあつきこと・いぬ（寒来暑往）
シュウシュウとあきはとりおさめ
　　　トウゾウとふゆはおさむ（秋収冬蔵）

Korean has a similar practice when reading Classical Chinese, and this article points to its similarity with English binominals which is especially outspread in Early Modern English.

"The inaudible and noiseless foot of Time" (Shakespeare: All's Well That Ends Well, V. iii. 41)
"The dark backward and abysm of Time" (Shakespeare: The Tempest, I. ii. 50)