Learn Hardcore German: Gefiltertes Wasser schmeckt mir besser als Leitungswasser. - Filtered water tastes better to me than tap water.

It’s capitalized only because it is the first word of the sentence. Normally it would be written gefiltertes Wasser (lowercase g), since gefiltert is an adjective/participle.

The ending -es comes from adjective declension:

gefiltert (from the verb filtern) is used like an adjective in front of Wasser.
Wasser is neuter, singular, and here it is the subject → nominative.
There is no article (das, ein, dieses, etc.) before it.

With no article before a neuter noun in the nominative singular, an attributive adjective takes the strong ending -es:

gefiltertes Wasser – filtered water (nominative/accusative, no article)

Compare:

das gefilterte Wasser – the filtered water
mit gefiltertem Wasser – with filtered water (dative)
kein gefiltertes Wasser – no filtered water

So: Gefiltertes = capitalized because of sentence position, -es because of strong adjective ending before neuter Wasser.

Why is it schmeckt mir and not schmeckt mich?

In German, schmecken works like “to be tasty (to someone)” rather than “to taste someone/something”.

The pattern is:

etwas schmeckt jemandem

etwas (the thing that has a taste) = subject (nominative)
jemandem (the person who experiences the taste) = indirect object (dative)

So in your sentence:

Gefiltertes Wasser – subject (nominative)
schmeckt – verb
mir – dative pronoun (to me)

You cannot say schmeckt mich here, because mich is accusative, and schmecken doesn’t take the person in the accusative in this meaning.

Other examples:

Die Suppe schmeckt mir. – The soup tastes good to me.
Schokolade schmeckt vielen Leuten. – Chocolate tastes good to many people.

Could I say Gefiltertes Wasser schmeckt besser für mich instead of schmeckt mir besser?

You can say für mich, but it sounds less natural in this exact sentence and slightly changes the feel.

Gefiltertes Wasser schmeckt mir besser als Leitungswasser.
→ Standard, idiomatic way. Very neutral, what people normally say.
Gefiltertes Wasser schmeckt besser für mich als Leitungswasser.
→ Understandable, but it sounds a bit influenced by English “better for me” / “tastes better for me”.

Für mich is more natural if the structure is different, e.g.:

Für mich schmeckt gefiltertes Wasser besser als Leitungswasser.

Here für mich is just a fronted phrase meaning “as far as I’m concerned / in my opinion”. It’s okay, but the core grammar of schmecken still prefers a dative person:

etwas schmeckt mir (dir, ihm, ihr, uns, euch, ihnen)

So for “tastes better to me”, schmeckt mir besser is the normal choice.

Why is there no article before Gefiltertes Wasser and Leitungswasser?

German often drops the article with mass nouns (uncountable substances) when speaking generally, not about a specific instance.

Examples:

Ich trinke gern Kaffee. – I like drinking coffee.
Milch ist gesund. – Milk is healthy.
Wasser kocht bei 100 Grad. – Water boils at 100 degrees.

Similarly in your sentence:

Gefiltertes Wasser and Leitungswasser are used in general, as types of water.
That’s why there is no article: it’s about “filtered water” vs. “tap water” in general.

If you mean specific water, you would use articles:

Das gefilterte Wasser aus diesem Filter schmeckt mir besser als das Leitungswasser hier.
– The filtered water from this filter tastes better to me than the tap water here.

Why is besser used here and not something like mehr gut?

In German, you don’t form the comparative with mehr + Adjective for normal adjectives. You usually add -er to the adjective:

schnell → schneller (fast → faster)
billig → billiger (cheap → cheaper)

The adjective gut is irregular:

gut → besser → am besten
(good → better → (the) best)

So “tastes better” must be:

schmeckt besser, not schmeckt mehr gut.

Also, don’t confuse besser with lieber:

besser = “better” (higher quality)
- Gefiltertes Wasser schmeckt mir besser.
lieber = “rather / prefer to” (used with verbs of action or with mögen / trinken / essen etc.)
- Ich trinke lieber gefiltertes Wasser als Leitungswasser.
  – I would rather drink filtered water than tap water.

In your sentence, you are talking about how it tastes, so besser is the right word.

Can I change the word order to Mir schmeckt gefiltertes Wasser besser als Leitungswasser?

Yes, that word order is completely correct.

Both of these are fine:

Gefiltertes Wasser schmeckt mir besser als Leitungswasser.
Mir schmeckt gefiltertes Wasser besser als Leitungswasser.

The difference is mainly in emphasis:

Starting with Gefiltertes Wasser puts the focus on what tastes better.
Starting with Mir can emphasize to me (maybe contrasting with what other people think).

In both sentences, the finite verb schmeckt is still in second position, which is required in main German clauses:

Gefiltertes Wasser / Mir = first position
schmeckt = second position
The rest of the sentence follows.

So you are free to alternate the order for emphasis, as long as the verb stays in second position.

What case are Gefiltertes Wasser and Leitungswasser in?

They are both in the nominative case.

Breakdown:

Gefiltertes Wasser is clearly the subject of schmeckt → nominative.
→ (Das) gefilterte Wasser schmeckt (mir).

With the comparison:

We can think of the “long” version as:
- Gefiltertes Wasser schmeckt mir besser, als Leitungswasser (mir schmeckt).

In that understood second clause:

Leitungswasser is again the subject of an implied schmeckt → also nominative.

So the structure is effectively:

[Nominative] schmeckt [Dative] besser als [Nominative] (schmeckt).

And mir remains dative throughout as the person who experiences the taste.

Why is als used here and not wie?

German makes a clear distinction:

Comparative (more/less … than) → use als
- besser als – better than
- größer als – bigger than
- schneller als – faster than
Your sentence:
- besser als Leitungswasser – better than tap water
Equality (as … as) → use wie
- so gut wie – as good as
- genauso teuer wie – just as expensive as
Example:
- Gefiltertes Wasser schmeckt mir genauso gut wie Leitungswasser.
  – Filtered water tastes just as good to me as tap water.

So:

besser als = correct Standard German
besser wie is common in some dialects, but is considered non-standard.

Why is Leitungswasser written as one word?

German loves compound nouns: several nouns (or noun + other elements) are combined into one long noun.

Here:

Leitung – pipe, line (in this context: water pipe)
Wasser – water

They are combined:

Leitung + s + Wasser = Leitungswasser

The -s- in the middle is a common linking element (Fugen-s). The rightmost part (Wasser) is the “head” of the compound, so the whole word is still a kind of water.

Other examples:

Haustür – house + door = front door
Zahnarzt – tooth + doctor = dentist
Waschmaschine – wash + machine = washing machine

All nouns in German are capitalized, so Leitungswasser is written with a capital L.

Could I also say Gefiltertes Wasser schmeckt mir besser als Leitungswasser schmeckt?

Yes, that’s grammatically correct, but in this case it’s more natural to omit the second schmeckt.

German often drops repeated verbs in comparisons if the meaning is clear:

Er ist größer als sie (ist).
Heute ist es wärmer als gestern (war).

Similarly:

Full form:
Gefiltertes Wasser schmeckt mir besser, als Leitungswasser (schmeckt).
Normal spoken/written form (with ellipsis of the verb):
Gefiltertes Wasser schmeckt mir besser als Leitungswasser.

You would usually only keep the second verb if you need extra clarity or emphasis, which isn’t necessary here. The short version is what people naturally say.