Here is an interesting and thorough comparison from Motorcycle USA: 2014 Heritage Softail vs Indian Chief Vintage.
The testers agree with comments above re power but not heat, comfort nor handling. To each their own. 
Nor noise. One said in the video the valve train noise took away from the experience of the ride.
My wife and I did two test rides at Daytona. The first on the entry level Classic. No bags, no crash bar no windshield. I wasn't planning on riding a Classic but showed up early for my ride and they needed a rider for one if the other rides so we went. I was concerned about not having a shield or backrest for my wife but it was actually an enjoyable ride. She and I both noticed the ride which contrary to the video on Greg's link, was very smooth. It also had gobs of torque and zero heat. I did notice a "rake" feeling when coming back to the parking area but nothing I wouldn't get used to as it was way less heavy feeling than my RG (of course, as it is).
Then we went on our second ride and I was first in line to get the Vintage (shield, bags and crash bar). I had previously arranged to have the detachable backrest they had on site for the Cheiftan to be mounted on the Vintage. It did fit but the diameter of the docking bars on the Vintage were smaller and it wasn't a tight enough fit so they were afraid to let us try it. They offered for us to ride a Chieftan (fairing) with the backrest but I wanted to ride the Vintage so I declined. I can also go back to the Indian dealer in Daytona now that Biketoberfest is over and ride their demo Cheiftan, which I will do. The parts guy at the dealer back in town (the rides were at the speedway) later told me the demo bikes were all Proto types and that could have been the difference. The bikes he had in the showroom looked to be identical in diameter on the docking bars.
The 2nd ride was almost the opposite. Right away we noticed the "ride" difference. My wife leaned up and said it didn't feel the same but she couldn't put it into words. I knew what it was and explained to her it was the engine. It was like a different bike. Both bikes had just under 3k miles but were totally different. The engine had a vibration to it especially when revving to higher RPM's on the straightaways trying to catch the group. The heat was also noticeable right away and by the time we returned from about a 10 mile loop, my left upper, inner thigh/groin was quite hot. I assume the shield was the difference here and maybe the bags as I'm sure they change the air flow around the engine.
Maybe the Vintage had been ridden most of its 3k miles under low, lugging RPM's and the plugs were fouled. Maybe there was some other problem but there was definitely a huge difference between the two. Night and day. I let the techs know when we got back.
There was one of the demo bikes, a Vintage also, that had a stage 2 kit on it. It sounded exactly like most Harleys. Also, you could see and hear the quick throttle response it had when the guy would get on it. Also, when the clutch was pulled in and he'd give a quick whack to the throttle the response was immediate. I spoke with the guy after the ride and he said he felt some heat but nothing like his 05 Ultra.
I took a couple of pictures with my phone of some of the bikes at the dealer and demo ride and as soon as I can I will post a few here.