Learn Hardcore Russian: Я люблю сравнивать старые фотографии с новыми. - I like to compare old photos with new ones.

Because люблю talks about a general preference or habit (something you like doing in general), Russian normally uses the imperfective infinitive for that: сравнивать.

сравнивать – imperfective: “to compare (as a process, in general, habitually)”
сравнить – perfective: “to compare (once, to finish the action, reach a result)”

With verbs of liking/wanting such as любить, нравиться (с инфинитивом), уметь, the infinitive is usually imperfective when it means a general activity:

Я люблю читать. – I like reading.
Она любит готовить. – She likes cooking.
Мы любим сравнивать фотографии. – We like comparing photos.

Я люблю сравнить is ungrammatical in standard Russian in this meaning.

What case are старые фотографии in, and why do they look like nominative?

They are accusative plural.

The verb сравнивать takes a direct object in the accusative: compare what? → старые фотографии.

For inanimate nouns like фотография, the accusative plural form is identical to the nominative plural:

nominative plural: старые фотографии – “old photos”
accusative plural: старые фотографии – “(I compare) old photos”

So they look like nominative, but function as accusative here.

Why is it с новыми, and which case is новыми?

Новыми is in the instrumental plural case.

The verb сравнивать (and сравнить) normally uses this pattern:

сравнивать что с чем
“to compare what (accusative) with what (instrumental with с)”

So in the sentence:

что? → старые фотографии (accusative)
с чем? → с новыми (фотографиями) (instrumental, with с)

That’s why you see с новыми, not с новых or something else.

Where is the word “photos” after новыми? Why is it just с новыми?

It’s simply omitted because it’s obvious from context.

Full, “long” version:

…с новыми фотографиями.

Russian often drops a repeated noun if it has already been mentioned and is clear:

Я купил старую книгу и новую.
Literally: “I bought an old book and a new (one).”

Same pattern here:

…старые фотографии с новыми (фотографиями).

English also does this (“new ones”), and Russian does it too, just without adding “ones”.

Could I say Я люблю сравнить старые фотографии с новыми?

No, that sounds wrong in standard Russian.

люблю + инфинитив → general liking / habit → imperfective:
люблю сравнивать

If you want to talk about a single, concrete act of comparing, you would use a different verb instead of любить, for example:

Я хочу сравнить старые фотографии с новыми. – I want to compare…
Я решил сравнить старые фотографии с новыми. – I decided to compare…

So:
Я люблю сравнивать… ✔
Я хочу / могу / решил сравнить… ✔
Я люблю сравнить… ✘

Could I use Мне нравится сравнивать… instead of Я люблю сравнивать…?

Yes, you can:

Мне нравится сравнивать старые фотографии с новыми.

Both are correct, but there is a nuance:

Я люблю… – sounds a bit more active, like a stronger personal preference or hobby: “I love / I really like…”
Мне нравится… – “It pleases me / I find it enjoyable”; often feels slightly softer or more neutral.

In many contexts they overlap and both are fine.

Can I drop я and just say Люблю сравнивать старые фотографии с новыми?

Yes.

Russian often omits subject pronouns when the verb ending already shows the person:

(Я) люблю сравнивать…
(Я) работаю дома.
(Мы) живём в Москве.

In writing, including я is neutral and slightly clearer. In casual spoken Russian, dropping я here is completely natural:

Люблю сравнивать старые фотографии с новыми.

Can I change the word order, for example: Я люблю сравнивать новые фотографии со старыми?

Yes, Russian word order is quite flexible.

Your version:

Я люблю сравнивать новые фотографии со старыми.

is perfectly correct. The meaning is basically the same: it just emphasizes the “new photos” a bit more than the “old photos”.

Some natural variants:

Я люблю сравнивать старые и новые фотографии.
(“old and new photos” as one pair)
Я люблю сравнивать новые фотографии со старыми.
Старые фотографии я люблю сравнивать с новыми.
(extra emphasis on “old photos”)

The original sentence has a neutral, straightforward word order.

Why are старые and новыми different forms if both refer to “photos”?

Because they agree with different cases:

старые agrees with фотографии in the accusative plural (direct object):
- (что?) старые фотографии – “old photos” (being compared)
новыми agrees with the (understood) фотографиями in the instrumental plural (after с):
- (с чем?) с новыми (фотографиями) – “with new (photos)”

Adjectives in Russian must match their nouns in gender, number, and case.
So the different endings show that “old photos” and “new (ones)” play different grammatical roles in the sentence.

Could I make this sentence singular, like “I like comparing one old photo with one new photo”?

Yes, you can make everything singular:

Я люблю сравнивать старую фотографию с новой.

Here:

старую фотографию – feminine accusative singular (direct object)
с новой (фотографией) – feminine instrumental singular (with с)

The grammar pattern stays the same:

сравнивать что? → accusative (старую фотографию)
с чем? → instrumental with с (с новой (фотографией))