Learn Russian: По-моему, цифровой фотоаппарат очень удобный по сравнению с аналоговым. - In my opinion, a digital camera is very convenient compared to an analog one.

The phrase по сравнению с (compared to) ends with the preposition с, which requires the instrumental case here. The word аналоговым is the instrumental masculine singular form of the adjective аналоговый. The noun it modifies, фотоаппаратом, is simply omitted to avoid repeating it from earlier in the sentence.

Is it possible to use the comparative adjective удобнее (more convenient) instead of this structure?

Yes! You could easily say цифровой фотоаппарат удобнее аналогового (using the comparative adjective followed by the genitive case). The structure with по сравнению с is just an alternative that lets you state a strong quality (очень удобный) while explicitly drawing a comparison to something else.

Why does По-моему have a hyphen and a comma?

Adverbs formed from adjectives or pronouns using the prefix по- and suffixes like -ому or -ему are always hyphenated. Furthermore, because по-моему (in my opinion) is an introductory word that shows the speaker's personal attitude, Russian punctuation rules require it to be separated from the rest of the sentence by a comma.

Could we use the short-form adjective удобен here instead of удобный?