Can all species that undergo aldol reactions also undergo Cannizzaro reactions? Ater all, the nucleophile can always attack the carbonyl group.
No. The Cannizzaro reaction only works for aldehydes with no $\alpha$-protons, benzaldehyde being a classic example.
For a start, ketones and any other species that can form stable enolates, such as esters or carboxylic acids, can undergo the aldol reaction or similar reactions like the Claisen condensation. However, the Cannizzaro reaction is limited to aldehydes because only they can disproportionate to form alcohols and carboxylic acids.
Secondly, the Cannizzaro reaction involves strongly basic conditions, typically using sodium or potassium hydroxide. Under these conditions an aldehyde with $\alpha$-protons will undergo deprotonation to form an enolate much more readily than nucleophilic attack on the the acyl carbon by a hydroxide ion.