There is no single best processing apple, because the three main outputs want incompatible things from the fruit.
For IQF dice and slices
Firmness is the constraint. The variety has to hold its cut geometry through dicing, blanching or an anti-browning treatment, freezing, and then a thaw in the buyer’s process. Varieties with dense, low-porosity flesh perform; soft, mealy varieties collapse and generate fines. Slow enzymatic browning is the second criterion, because it reduces the intervention needed between cutting and freezing.
In Ukrainian orchards the firm-fleshed commercial varieties grown for the fresh market generally double as the dice and slice raw material, which is convenient: the same block can be sorted, with the cosmetically saleable fruit going fresh and the rest going to the cutting line.
For juice concentrate
Sugar and acid, in that order. High soluble solids reduce the water that has to be evaporated, which is the dominant cost driver in concentrate production. Acidity matters because the finished concentrate has to sit inside the compositional ranges buyers assess against the AIJN Code of Practice, and a blend that is flat will be corrected by blending in higher-acid fruit rather than by addition. Yield at pressing is the third factor, and it is as much a maturity and storage question as a variety question.
This is why concentrate producers blend. A single-variety concentrate is unusual; a blend engineered to a target Brix, acid and colour is the norm.
For puree
Breakdown behaviour. The variety should soften predictably under heat and pass the finisher without leaving excessive residue, and it should hold colour through the heat treatment. Some varieties that make excellent dice make poor puree precisely because they resist breakdown.
The practical answer for a buyer
Do not specify a variety unless you have a genuine functional reason. Specify the functional outcome, firmness after thaw, Brix and acid, colour and breakdown, and let the processor select and blend against it. Variety-locked specifications narrow the supply pool and raise cost without reliably improving the result. The frozen apple record sets out the functional parameters that matter.