Hi and welcome!
The ODDA bed definitely has that particle-board, inexpensive construction, good for kids rooms look, and the trundle is really a giant mattress sized drawer. There is no box spring or mattress frame or anything like that, just the wood construction of the box and drawer.
We have the Lycksele full size sofabed in our daughters room which is much more bed-like. I like that it folds out into the room, which is different than the Beddinge which folds in half the long way. I don't like adult beds that are against a wall so unless you turn the Beddinge 90 degrees, you will most likely have one side of it up against a wall. So one of you will have to crawl over the other to get out of bed.
The Lycksele comes with several mattress options (that's the price differences) but we've got the cheapest with a 2 inch memory foam on top and it is quite comfortable. Guests were quite pleased with their night's sleep!
The only other issue you might have with the sofabed is that there are no arm rests, so when using it as a sofa it isn't all that comfortable to sit on since there's nowhere to put your arms. I have the same complaint about slipper chairs although they seem hugely popular.