Straw is actually considered preferable by many. In composting/mulching circles it is often called the perfect one. But it is often far more costly than hay in many parts of the country and not at all available in some parts.

Hay has an added benefit over straw in that it provides N to the soil as it decomposes. Straw, as a carbon, does not, and requires the addition of extra N to decompose. But the hollow stems of straw prevent it from matting as much as hay does. Either works well so it boils down to which is more readily available to you at a reasonable costs.

Dave

I actually get straw for free as I have a neighbor who has an abundance of bales, which he was using as a temporary barrier wall, and has offered it to me. Do I need to be concerned about where the straw is coming from if I don't know the source... Basically I would be worried about any potential pesticides if I don't know where its coming from. Or is that not something typically used in straw?

I also prefer straw especially if it is free:-). But you might get some rye or wheat growing in it . Also with the hay you might get weeds.
My other favorite mulch is pine straw. Down in GA you can get plenty of it at reasonable prices. HD used to sell it trucks load of it. It is the most common landscaping mulch down there. But Up here in PNW all I can get is pine bark mulch or nuggets. @ 2 bucks per cubic foot. Not bad.

Sey

<Basically I would be worried about any potential pesticides if I don't
know where its coming from. Or is that not something typically used in
straw?>

Herbicides is more of a concern than pesticides. Longer lasting and more damage. But neither is commonly used with grain crops IME and if the bales are aged more than a year old they'd be of minimal concern.

Dave