Michael reaction or nucleophilic attack at the alpha carbon of an alpha-beta-unsaturated ketone?
An $\alpha,\beta$-unsaturated ketone is electrodeficient at the $\beta$ position. This can be seen if you draw the resonance structures of such a molecule.

The $\beta$ carbon is thus a good site for nucleophilic attack. But, as you know, carbonyls are also prone to nucleophilic attack. To discriminate between the two, you need to look at how the reaction is controlled, either thermodynamically or kinetically.

In a kinetically controlled reaction, the product that is formed fastest predominates. In a thermodynamically controlled reaction, the predominant product is the energetically favored one.

A Michael addition is a 1-4 addition, where a nucleophile attacks the $\beta$ carbon, and produces the thermodynamically favored product. On the other hand, a 1-2 reaction (on the carbonyl) gives the kinetic product, and is obtained at low temperatures.

Why is the 1-4 product thermodynamically more stable? Because the resulting product benefits from keto-enol tautomerism, which results in lowering the energy of the system. Usually, the more resonance forms a compound has, the more its electrons are delocalized, the more stable it is.

Draw the resonance forms of the 1-4 and 1-2 products, and see.



You asked for specific affinities of different organometallics in 1-4/1-2 additions. My knowledge is that organocuprates ($\mathrm{R-CuLi}$) will perform Michael additions, and that organolithians seem to prefer 1-2 addition. Also, according to this source, Grignard reagents do not seem to have a preference.

My take on this is that the cuprate is less reactive, and therefore can form the thermodynamic product, whereas the lithium reagent is so destabilized that it reacts right away.