I have used 6mm (1/4), 5mm (about 3/16) and 4mm strips for different kayaks.

The only possible advantages I can see of 1/4"strips is increased stiffness and a little more thickness to work with if your strips are very badly fitted and need a lot of sanding. However 5mm and even 4mm is plenty stiff enough and you would need to be very careless to need to sand away most of your strip.

I find 5mm is easier to bend to shape and easier to clamp in place. I use a few U shapes bits of timber clamped to the forms to hold the strips and masking tape to hold them between forms. If the strips have been bent using a heatgun to reduce the stresses involved, masking tape does a pretty good job.

Most of a kayak is usually easily built with 3/4" strips with a few cut thinner to deal with the tight curves. I can't see any advantage in using narrower strips for the bulk of the kayak.