Q. Which type of pile cap transfers loads equally to piles, flexible pile cap orrigid pile cap?

Loads from columns transferring to pile cap persuade tensile forces at the bottom of the cap. For example by using truss analogy to analyse a pile cap sitting on two piles with a column at the centre of pile cap, tensile force at the bottom is proportional to pile spacing and is inversely proportional to depth of pile cap. Bottom reinforcement is designed to resist tensile stressed produced from loads in columns. Occasionally reinforcement can be designed at the top of pile caps that serve as compression reinforcement. This kind of reinforcement is essential in case there is a limitation on the depth of pile caps. In the same way shear reinforcement is introduced to the pile caps in case there is a restriction to the depth of pile caps. 

Consider that loads are applied at the centre of a pile cap.

For the case of rigid pile cap, due to the effect of interaction of individual piles, central piles tend to settle more than edge piles when pile cap is under loading condition. For the pile cap to be rigid, local deformation of central piles wouldn't take place. In its placestiff pile cap would transfer the loads from central piles and redistribute them to outer piles. So piles at the edge take up a higher fraction of total loads and are subjected to higher axial and bending loads in case the pile cap is stiff. In the extreme case, side piles may take up as much as about two to three times loads in the central piles and this may lead to failure of these edge piles. 

For flexible pile cap, load taken up by individual piles are different since the deformation of pile cap enhances non-uniform distribution of loads among piles. Piles closer to the load tend to share more loads when compared with those that are located far away from the loads. The difference of loads persuaded in piles increase with flexibility of pile cap.