OK, still trying to decide on my and wife's phone upgrade. Currently have HTC Tunderbolt. Which phone would you recommend to your parents? (Yes we are not spring chickens

) S4 or the S3 or wait for the HTC One? Just looking for your opinions. Thanks.
Hard to say. Things to consider: With HTC you are already used to Sense (the user interface) so the learning curve is considerably less. However, the S3 and S4 have an Easy Mode which trims down the User interface and is aimed at new smartphone users. Out of the box Samsung has a lot of tutorial pages, meaning when you turn it on for the first time, it pops up a teaching page that has a diagram of what to do for X feature. HTC I believe, has the same thing. Performance specifications are roughly the same.
I am a Samsung user, and I agree that the screen on the HTC is better. Arguments have been started over photo quality, (I don't take a lot of pics, so I don't care). Personally, I like having, at the very least, an SD card slot. I like having some things separated from my internal storage, like wallpapers, music, back ups, and the pictures and videos that I do have, to allow more space for Apps, which for the most part, can only be stored on the Internal Storage.
The HTC and the S4 should see support for a while. The S3 is about halfway through it's life. It will most likely get Android version 4.2, but 4.3 in my opinion is questionable, and if it does get 4.3, anything higher is highly doubtful.
I would say this: Take your current phone. What do you like about it? What do you hate about it? Make that list, and see what HTC and the S4 both offer to meet your needs. (I suggest the S4 due to support from Samsung. If money is an object, get the S3)
No matter what, you are choosing a top of the line device, or in the case of the S3, a former one, which is still very solid. Best of luck in your shopping, have fun playing, and most importantly, choose a device that YOU like, and if someone has a beef that you picked X over Y, smile and walk away.