There isn’t really any differences between those two sentences. The latter sounds slightly more formal than the former to my ears.

Yes, the sentence meaning is almost the same, the exact translations would be:

The pollution is worse than last year

The pollution is nastier than last year

But the second sentence is not good talk, french language doesn’t use plus mauvaise with pollution it could be used with temps or météo (weather) for example. Why? because pollution is a negative situation already, so why using nastier, there is not a lot of cases where you will use nicer pollution, isn’t it? On the other hand, weather could be negative or positive situation.

Aucune des deux phrases ne sonne bien à mon oreille. Et la seconde ne se dirait pas. S’il est question de quantité de pollution je suggère : « il y a plus de pollution que l’année dernière ».

Pour ce qui est des emplois respectifs de pire et de mauvais, tu peux regarder la banque de dépannage linguistique du Québec ou le Larousse.

There is some slight difference, because pire can mean plus mauvaise but also de plus mauvaise qualité, or plus nuisible, plus pénible, plus néfaste.
In this particular case, plus nuisible or plus néfaste (and therefore pire) are better suited than plus mauvaise.

However, something is disturbing in your example because, except for specific cases, only fluctuations in pollution levels are relevant; pollution (which basically means “introduction of harmful substances or products into the environment”) is an abstract concept which usually doesn’t change over time. So in this case, you probably want to say:

Le niveau de pollution est pire que l’année dernière.

Or simply:

Il y a plus de pollution que l’année dernière.

But if you compare qualities rather than quantities, both your sentences are fine (with a preference for pire for the reason mentioned above).

The adjective mauvais has both a regular comparative plus mauvais and an irregular comparative pire. The irregular comparative is the most common one. Furthermore, pire is sometimes used as a comparative even in cases where mauvais would not be used, but a different adjective with strong negative connotations. I have a hard time coming up with hard rules on when to use plus mauvais and when to use pire. The Trésor de la langue française describes pire as “surtout dans l’ordre moral” (especially in a moral sense). If in doubt, use pire.

Given your example sentences, I would use pire, without hesitation. “La pollution est pire que l’année dernière” is a sentence that I would use with no hesitation, a natural translation of “The pollution is worse than last year”. « La pollution est plus mauvaise que l’année dernière » is not something I would normally say, because I do not quite feel that the adjective mauvaise applies to pollution. Pollution is bad in a generic sense, this year like any other year. I might say “la pollution est plus gênante” or “la pollution est plus visible” or “la pollution cause plus de crises d’asthme”, if I wanted to focus on a specific aspect of why pollution is bad.

It is possible to make a difference in meaning between the two sentences. “La pollution est pire” could mean two things: a higher level of pollution, or that the same level of pollution has graver consequences. I understand “la pollution est plus mauvaise” as having the latter meaning, which is rather odd; it is not completely unambiguous either.

You can see that there are very few hits for “pollution est plus mauvaise”” on the web: only three unique hits, one in the sense you intend and two comparing pollution with another harmful concept (cigarette smoke). In comparison, “pollution est pire” is fairly common; many of the top hits are about pollution being worse in one place than in another, which is very close to your sentence.

I’m surprised that several contributors here consider the sentence with “plus mauvaise” idiomatic; I don’t, and the evidence I can find supports this.