I gave it a trial run a couple of years ago, as I was attracted by the novelty of the idea. It takes a little bit of setting up, as the bales need conditioning for a couple of weeks prior to planting by fertilising and watering. This starts the decomposition process and generates the heat that allows sowing or planting earlier than in the ground, and therefore earlier harvesting, and increases yield. I planted tomatoes, cucumbers (in the greenhouse), lettuce and chard in a total of 8 bales, stood on end, and used the same seed varieties to grow in my usual manner, in pots in the greenhouse, and in the ground.
I found that yields were certainly a little better in the bales, and I was harvesting two to three weeks earlier, but the major improvement was the reduction in watering requirements, as the straw holds onto water much better than compost. The one downside was that the neighbours' two cats seemed to find the bales really attractive for sleeping on: I'm assuming that was because of the heat generated; and so I ended up with some ruined crops in the bales outside of the greenhouse, together with bales knocked over on a couple of occasions and straw blowing around the garden. I will definitely use the method again, perhaps trying some bird netting or some willow screening to deter the cats (I tried orange peel, but they don't seem to mind that!).
The jury is still out here about the balance between any increase in yield and the cost of the bales, and so another trial is definitely warranted: not that the bales are expensive per se, but I make my own compost, so even paying a nominal amount for the bales increases the cost of my crops. However, if the yield increase is significant, that combined with earlier harvesting and reduced watering, will certainly tip the balance.
Other users of this system also report reduced impacts of pests, particularly slugs and weevils. I don't have a huge problem with slugs, despite the fact that I am totally organic, largely due to the fact that many of my more susceptible crops are grown in containers, but also, and probably more significantly, due to the hedgehogs that are regular visitors to my garden. However, over the last couple of years, I have noticed an increase in vine weevils, so if straw bale growing could help to reduce their impact, I would be a happy bunny.