I have read that wood mulches are good for veggies, and flowers. Pine straw and pine bark are not good for the last two, but are good for trees and shrubs. I think I would stick with your hay - it will break down MUCH faster and improve your soil much more. One of the reasons many landscapers use pine bark is that it is very slow to break down. If you have clay soil and want to improve the texture, mixing in "soil improver", very fine pine bark, is a good way to do so - it lasts for a while before it finally does break down.

If you do use it, it won't add much in the way of water retention to the soil, as it doesn't hold much itself. It will help the soil hold moisture. Its tendency to float away in heavy rains may be another reason not to use it.

Dr. Alex Shigo, once the chief of research for the US Forest Service, found that woody material tended to make soils fungi dominate which tended to make them more acidic which trees and shrubs prefer. Vegetative mulches, straw, leaves, etc. tended to make soils more bacterial dominate which is the more near neutral which flowers and vegetables prefer. The link below will get you to Dr. Shigo's work.

Here is a link that might be useful: Dr. Alex Shigo