Will a new unlocked iPhone work with any carrier

That wasn't exactly the question I had. The original question was a replacement iPhone 6 that the store gave me because when I took it my original iPhone 6 in for the battery exchange the battery was already swelling in the case and the store person stated that they weren't allowed to open it at that point so they gave me a new replacement 6. I didn't know if there might be an internal difference in the phones or not (TDMA, CDMA). I'm selling this new iPhone 6 which has never been activated or sim installed since I already purchased a new X. I just wanted to be sure so when I sold it I wasn't giving the buyer bad info and it would work on any system.

Your second sentence answered my question. Also since I knew I was going to replace the 6 with a X I called my carrier, Consumer Cellular, and had the 6 unlocked since I had it for 4 years. I was taking advantage of Apples battery exchange program and was going to sell or donate the 6 after I had a new battery installed. As it turned out the battery in my 6 was just starting to swell although the phone was still working fine. The Apple store person stated that since swelling was occurring store personnel weren't allowed to open it thus they would give me a new replacement 6 for the cost of the battery which was 29.95 as I remember. So the replacement phone was never activated or a sim card inserted. I called Apple support and they verified that since it was never setup, activated and sim installed that it was an unlocked phone compatible with any carrier.