This is Pandora's shipping crate for me.
There are two parts to this argument, which people are mixing up: dual screen and touch screen. It's perfectly possible to have one without the other, but most people won't have tried to think of that.
My problem with a dual screen is that this is a PC, not a DS. A PC has one huge screen, whereas the DS was designed specifically for two tiny screens (and thus is allowed to have one screen for the overworld and another screen for a menu/Pokétch - the PC is not). The dual screen is simply unnecessary fora PC game, because the screen can easily be redesigned to compensate for whatever the second screen may offer.
Another issue with the second screen is that everyone seems determined to copy HGSS pixel for pixel, rather than doing something good with it. I thought having the Pokétch in the second screen while idle was brilliant - it's a hugely easy way to check your party, use Itemfinder and scan for legendaries. Having a menu there is just stupid, because you need to click to get to it, and it just reminds you that this is a game (you know what I mean) by sitting there with its "Save" and "Options" buttons even when you're not using it.
Another complaint I have with it is the claim that a dual screen somehow makes Pokémon "better". were the Gen 3 games really that horrible to use? No! They worked just fine, thank you. The redesigned happened because the games went to the DS, NOT because the interfaces were in any way flawed. There were all of three buttons you needed to remember - the "okay" button, the "back" button and the "open menu" button (with the "use registered item" button as an optional fourth). I would feel ashamed if you're complaining this is in any way difficult to remember.
One suggestion I will make is that a second screen absolutely need not be "the same size again, directly beneath". It can be short and wide, above or below, long and thin, on either side, a border around the main screen, anything you can imagine. One of my favourite ideas is to have a short bar underneath the main screen that contains text messages when talking to someone, and the party Pokémon icons/HP bars when idle. It doesn't take up much space, is very useful and practical in and of itself, is remarkably different to anything else going around at the moment, and doesn't distract nearly as much from the actual playing of the game. Having a huge second screen, without using it to the fullest in all parts of the game, is just not a good idea.
Now, the touch screen. For most people, this is a synonym for "the second screen", and once again I remind you that it really isn't.
If anything, a touch screen in a game like this is even more unnecessary than a dual screen. The simple reason is that the entire game is played with two hands on the keyboard (arrow keys and CXZ whatever). Having to move over to the mouse every time you want to pause the game or go into battle is just not comfortable. The games worked perfectly well before with their keyboard-only controls, and I strongly suspect that the only reason they have touch screen capability is because they have to because they moved to the DS (i.e. rather than because a touch screen is simply better to use). The fact that, in the DS games, all the menus can be just as easily navigated with the D-pad anyway should be a clue that the touch screen part is a novelty rather than an integral part of the game.
Then we remember that most people think "touch screen" = "second screen", and thus only implement the touch screen features on half of the game's window. That's just stupid. Why must I be restricted to doing all my clicking in the bottom half of the window? And if you answer "there's no reason to click up there", then I say that's just because you're using the old boring restricted layout the real games use, rather than using a bit of imagination and coming up with better layouts. For one, you can make much better minigames if you allow the whole window to be touchable.
By now you're thinking I despise any kind of change to the games, and that I think Gen 3 was the pinnacle of programming. Well, you're wrong (even though there was nothing wrong with how Gen 3 worked in the first place). An extended screen would be great if it's implemented properly, and the same goes for a touch screen. My gripe is with how they're currently used.
They're used by the people who just want to emulate HGSS pixel for pixel, and so there's no innovation there (please don't start scouring for counter-examples - I know I'm generalising). As it stands, the DS layout and interactivity is really quite unsuitable for a PC game, for the reasons I mentioned above plus many others I couldn't think of. Yet people insist on sticking to it, for the sole reason of "HGSS is the newest game, and I want to be just like it!". The same goes with the tileset argument. Now excuse me, but that's just not a good enough case.
And put it this way: if you're good enough to put in a touch screen and/or second screen, you're more than good enough to move things around a bit and improve the interface. That's the easy part. This just makes the lack of innovation even more annoying - it's like a painter creating a masterpiece but not putting it in a frame.
If you want your game to be good, do it differently. HGSS is not the pinnacle of Pokémon achievement, no matter what you may think. You are not bound to its limitations. Some of its design rules can be bent. Others can be broken. Free your mind.