$5 a bundle? That size? Geez, that is cheap. I would opt for the softwood, as it probably has 60% or more of the heat as the hardwood. The mills where I used to live put out bundles of remnant fir cuts and log ends, but they wanted money for them. More like $50 for a 4x4x4 bundle, u-pick.
As for burning it in an OWB, that is one of the great things about OWBs. You can burn rotten, wet, green, buggy, trash wood, rounds, construction wood remnants, barn wood, naily wood, mill ends, furniture wood, branches, brush, cardboard, junk mail, and good old fashioned seasoned and split (or unsplit) firewood. And softwood and hardwood, and just about any wood except treated wood and particle/strand board.
The biggest thing that sold me on the OWB that we bought when I was living with the ex was that the OWB took unsplit, long logs. I cut firewood into two to three foot lengths, and we never split anything under a foot in diameter. What I did split was large, just small enough that the ex could lift and get them into the boiler. That saved a HUGE amount of time as we were burning 10 cords a year.