Information on the following chart was extracted from a comparison of types of pillows on Sleep Like The Dead, an independent review and evaluation site for mattresses and pillows.

Shredded memory foam is rated higher in most categories, though single-piece memory foam rates higher in some. Comparing these to verified customer review ratings of individual pillows (such as on Amazon), it is evident that shredded memory foam has the advantage for head pillows and full body pillows.

Shredded vs. 1-Piece Memory Foam

As of 11/15/2017 

Affordable D C+ Prices are often $30-$90. Shredded averages about $57 and 1-piece about $50. Paying higher price does not necessarily result in higher satisfaction.
Durability / longevity B- C Shredded tends to last longer given its ability to be fluffed. Both types will lose “memory” and support over time. Expect on average a 3-4 year lifespan.
Less (neck) pain B B- 18% of owners say their pillow results in less (neck) pain. About 8%, however, report increased pain, often due to excessive firmness or lack of support.
Supportive B B- Most owners say their memory foam pillow provides adequate or better support and holds its shape.
Minimizes pressure A A- Memory foam contours to the head / neck better than other pillows resulting in more equal weight distribution and above average pressure relief.
Moldable B D+ “Moldable” means the pillow can be easily altered or scrunched to increase comfort / support. Shredded, unlike 1-piece, offers at least some moldability.
Cuddly B+ C A “cuddly” pillow is soft and huggable – not hard, rigid, stiff or oddly shaped.
Contents won’t shift / clump C+ A A strength of one-piece memory foam pillows. Shredded has less stable contents which may shift somewhat during the night.
Back sleep friendly B+ C+ Loft usually cannot be made significantly lower or higher (by flattening or scrunching) so some back sleepers may be dissatisfied.
Side sleep friendly B+ B Loft usually cannot be made significantly lower or higher (by flattening or scrunching) so some side sleepers may be dissatisfied.
Stomach sleep friendly C+ D+ Loft is often too high to be ideal for stomach sleepers, especially sleepers of small size.
Not a heat trap B- D+ About 5% of owners (1 in 20) of the shredded type report excessive and bothersome heat retention vs about 11% of owners (1 in 9) for the one-piece type.
No initial odor / off gassing D+ D+ 7%+ of owners (1 in 14) report significant off gassing – a chemical-like odor occurring due to manufacturing & packaging. It often ends after a few days but can persist longer. Headaches, nausea, eye / throat irritation, sweating, insomnia & asthma from off gassing occur for about 2% of owners.
Short break in B- C Break-in time is similar to that of the average pillow.
Easy to lift, move C D+ Memory foam pillows, especially the one-piece type, weigh at least average, usually 3 to 5 lbs.
No noise B+ B+ Some covers may make a rustling sound when compressed. The pillows themselves are silent.
Fewer allergies B+ B- The foam is antimicrobial and resistant to allergens. Dust mites reportedly do not eat the foam but still may live inside to feed on shedded skin cells.
Easy to maintain C A Shredded memory foam pillows may require occasional fluffing. One-piece types do not.
Easy to clean B+ C The one-piece type should be spot cleaned. The shredded type can usually be machine washed.