Not a fan of the H-Bar ...
I changed out my drops for a Jones H-Bar before my most recent tour. I rarely (like never) used the drop position, and it made sense to change to the "cruiser" style of the H-Bar. Of course I now also needed to change my shifters and brake levers too, but the cost wasn't that much so it all made sense to me.
I immediately had a problem with hand numbness. I have toured several thousands of miles on my drop bars with no issues, but after the first full day on the H-Bar, I had Ulnar nerve issues that have persisted for nearly three months. I had to suspend my tour after a couple of weeks as I lost the use of my right hand. My sports doc has me off the bike until the situation resolves itself. My fingers are slowly getting feeling back but it's been tough to see the summer pass by and not be able to ride.
My story may not be the same as others using an H-Bar as I've seen postings from people who successfully changed to the H-Bar. Perhaps it's a peculiarity of my hands, who knows... At any rate, I plan to replace my Jones H-Bar with drops so I have one to sell complete with MTB shifters and brake levers. Make me an offer!