First off, if you are concerned about radiation levels, then cellphones should be pretty low on your list of concerns compared to many, many, many other things you encounter in your daily life. Suffice it to say, if you live anywhere near a cell tower or radio station (close enough to receive a signal) then you are probably exposed to more radiation than any cellphone will give you anyways. And gawd forbid if you have a smoke detector in your home!
Now that I have that off my chest, lets talk makes and models.
I see only two makers as being worth considering; Samsung, and Motorola. HTC is solid, and occasionally has a cool and unique gimmick, but they are definitely not the best. Both Motorola and Samsung are top-tier, and every “The Best smartphones” list has a lot of Samsung and a bit of Motorola on it, but many seem to lack HTC.. for a reason. That reason is that they are mostly a mid-range phone maker, so it’s like comparing a Ford to a Ferrari.
The most recent lists I’ve seen place the Motorola Razr HD, Samsung Galaxy, and of course iPhone at the top. If call quality or battery life are of interest to you, the HTC One loses to those three, and unlike most other Android phones (but like the iPhone), the storage is non-expandable.