This is an incredibly sweeping generalisation - and varies hugely from speaker to speaker - but in my experience, ceramics typically have a more pronounced midrange and a more immediate, transient attack. AlNiCos are a little more 'happy face' EQ...thicker lows and more bell-like top, with less in-your-face mids and slightly more compression overall. I tend to say ceramics sound more 'rock and roll' and AlNiCos sound 'posher'; most people say ceramics are more suited to loud live playing - often with a good amount of gain - and AlNiCos are more suited to studio use and/or for clean/low gain stuff. AlNiCos can sound a bit 'fizzy' with gain because they're less rolled-off up top; ceramics can sound a bit spikey/lo-fi with clean tones because of their mids.What does Alnico give you over similar Ceramic speakers?
Also worth noting that AlNiCos are usually much bigger/deeper than ceramics - so won't fit in every combo (I had to modify my H&K Puretone chassis to accommodate an AlNiCo as the back of the speaker was fouling the preamp tubes.
As I said - HUGE generalisations there, but in my experience they're largely true.