I’m going to speak from a Greek perspective, and I hope that Turks and Albanians will weigh in.
The hostility between Greece and Turkey is very old, and definitional to their identity. They came to regard each other as the Primordial Enemy. (Hence the immortal line on Ekşi Sözlük: “The good old days, when Greece was the National Enemy.”)
Greeks really did come to define themselves as Not-Turks. The world was viewed through a binary lens of enmity, and had been since the Seljuks came to Anatolia; the credal difference between Islam and Christianity was all enmeshed with the ethnic difference (and in reality took priority over it). And there are defining incidents in Greek history which can serve as rallying points for that enmity. 1071, 1453, 1669, 1821, 1897, 1923, 1974.
Enmity between Greeks and Albanians just does not have that kind of heritage. Until the forced islamisations, Albanians were another annoying Balkan ethnicity. In situ in Albania, there were yet another people with an uncouth language for the Byzantine elite to look down on. As the Arvanites, they were warlords and settlers in Greece; they were stereotyped as pigheaded, and either admired or feared as warriors, but they were close-by neighbours.
Once the islamisations happened, Muslim Albanians were Turks. The Millet-based split was total; to Greeks, Muslim Albanians were Muslims first, Albanians second. Hence the confused appelation Turkalvani, which does not mean Turkish Albanians at all, but Muslim Albanians. In the Greek War of Independence, Orthodox Arvanites fought Muslim Shqipetars; they spoke the same language (maybe in a different dialect, maybe not); but as far as Greeks were concerned, the Arvanites were Greeks, and the Shqipetars were Turks.
That’s why any enmity of Albanians and Greeks is pretty recent. A notion of Albanian nationhood was stymied through to the end of the 19th century, because not only the Greeks, but the Albanians themselves regarded themselves as Christian or Muslim first, and Albanians second. That’s why it was so important for Albanian nationalists to proclaim that the religion of Albania is Albanianism: without Albanianism, there could be no Albania.
And hate to say it, but because of all that, Greeks have hardly noticed Albania as an enemy. Anything up until 1912 was chalked up to the Turks—including Ali Pasha of Ioannina. (How many Greeks realise he was Albanian? How many care?) The raids of the Christian Arvanites against their neighbours, which gave Greek its word for “plunder” (πλιάτσικο < plaçkë “thing”—plaçkë e luftës “thing of war” is implied) have been long forgotten.
There was an ongoing enmity against Turks until recently (and of course, the atavistic stuff still lurks in the collective subconscious, despite the Thaw). In the face of a bogeyman that imposing, any hostility against Albanians from Greeks was secondary, and localised. (And I know very well that Albanians have not felt the same way.)
Albanians became prominent in the popular conscious again with the mass migrations of the 1990s. There was a lot of hostility, and I’ve heard reports that the Arvanites were particularly hard on the Albanian migrants: they had something to prove. But it was really not the fear and existential stuff that was invoked with Turks; it was looking down on them.
Since then, the reaction has gone two ways (from what I gather from a distance). On the liberal side, the Albanians are the model minority, admired for their work ethic, and even seen as a welcome addition to the polity. (That’s a pretty extreme view for Greece, of course.) On the reactionary side, well, one of the favourite chants of the thugs is Δεν θα γίνεις Έλληνας ποτέ, Αλβανέ, Αλβανέ-έ-έ “You’ll never be a Greek, Albanian, Albanian!”
But from memory, hostility towards Albania has never roused the level of ire or passion that hostility towards Turkey has.