It absolutely does not make a difference to the plants,in my opinion. But you might find one easier to use than the other. I have taken to using pine straw. It is easy for me to handle and haul, to spread in the garden, to move to plant new things, and to mow around without sucking up chunks of wood mulch with the mower. Most of my beds are not bordered but just come down to the grass. Some of my beds do have wood chip or shredded bark mulch, some of it was free from the county but very hard work to haul and spread. Grass clippings work well too. I recently was reading Renegade Gardener website and he suggests bark chips or shredded bark mulch I think for the shrub and tree areas, and something like cocoa bean hulls or other easy to decompose mulch like grass clippings for the perennial or flower beds. Right now I am liking pine straw, altho I just cannot pass up anything free, so I think I'll get more free bark mulch in the spring. It's too hot to haul it now.
Laurie

Hi my flower garden is just like yours, shade and heavy clay soil. I use pine needles and am very satisfied. BUT, the needs are free! since I have a pine tree grove right by. I've used the pine needles for the last 5 years on my veggies and flowers and have seen no adverse reaction to the acid in them.

Pine needles are mulch, just as wood chips, shredded leaves, compost, or anything else you lay down on the soils surface would be. Now putting a mulch of anykind on a soil that is soggy will create more problems than it will solve since one of the reasons to use a mulch is to aid in retaining soil moisture. Before putting any mulch there find out why the soil is soggy (drainage issues?) and solve that problem, and then add the mulch.