Alghero in Sardinia, being the Catalan-speaking area most farthest away from Catalunya, how is their variant of Catalan different? I would think more similar to the Balearican variant.
We could sum up the characteristics of Alguerese in these:
It's Eastern Catalan (there's two main blocks of Catalan: Eastern and Western), closer to Eastern Catalonia
It has influence from all varieties of Catalan
It developed from the 15th century Catalan in a separate location, and after the 17th century the contact between l'Alguer and the rest of Catalan Countries faded. So Alguerese has kept characteristics of Old Catalan that were lost in the rest of territories, so it often sounds "ancient" to the rest of Catalan speakers
It has influence from Sardinian and Italian
Alguerese people descend from people who came from Eastern Catalonia (areas between Tarragona and Barcelona) in the late Middle Ages, for this reason the "base" of Alguerese Catalan is the Central Catalan of the 14th-15th centuries.
Until the 17th century, people from Catalonia (including Rosselló/Northern Catalonia), the Valencian Country and the Balearic Islands moved to l'Alguer, so in some ways Alguerese mixes characteristics of the different variants. But after that, it stopped having close relations with the rest of Catalan-speaking countries.
For this reason, they still use some words that seem "ancient" to other Catalan speakers, because we don't use them anymore but they do.
For example, in Alguerese the masculine singular article is "lo" (like in Medieval Catalan), while in most of the other Catalan-speaking countries it's "el", though in Western Catalonia they also use "lo" (check a map of that in this post). The same happens with words.
And of course after that, there's the Italian influence. It's quite noticeable in the accent of most Alguerese Catalan speakers (though some more than others).
Besides a few words though, we can understand each other without trouble. From time to time, there might be a word that's different (like in any other dialect), but in general it's not difficult. If you're not used to the accent, at first it might seem confusing, but very quickly you get used to it and there isn't problem to understand each other.