Those two are definitely incompatible. So you must use the matching dongle that came with each remote. But as I said, you can continue to use both simultaneously if you want. I found that the one on the left would wake my PC reliably, but the one on the right would not. So I also used both for years.
The thing I like about the old Ortek (the one on the left) is the integrated mouse. If you prefer your old remote, I have a couple like new that you could have for the price of shipping if you want ($4 or so). I only use the dongles since I have universal remotes. So either you take them or my wife throws them out. PM me if interested.
for the info on these remotes, it's just what I was looking for. If there were a "thumbs up" smilie, I'd be putting it right here.
It'd be a shame to throw out perfectly good remotes, but wife is very happy with the HP model as the buttons are bigger and easier to find in the semi-darkness. Thanks for the offer, though. Hope they find a good home.