Playstation 2 original
Tray-loading mechanism
The original PS2 has a tray-loading mechanism. You press a button, and the tray electronically comes out. It gives the PS2 an advanced appearance of technology.
Larger
You get more PS2, with the original PS2, than the slim PS2, because it's bigger. Looks solid, and has a nice, rectangular shape to it.
Nice blue "PS2" font on the top
Really attractive. Looks nice from a distance.
Fits in a nice, blue, vertical stand, and horizontal stand
When the PS2 sits on the blue, vertical stand, it looks really, really sharp. The blue stand really fits in with the blue font on the system. It gives the PS2 a nice, sharp, cut look. It's like vertical rectange, with two right triangles, on both sides, to give it a nice, geometrical shape.
Durable
The bigger size means that the PS2 is a lot more durable. It has thicker plastic than the slim PS2, and seems to be of better quality.
Costs more to manufacture
Because the original PS2 costs more to manufacture, it could mean that the slim PS2 is cheaper, and of lesser quality.
Plays all, or almost all, PS1 games
I believe that the origianl PS2 is fully backwards compatible with all PS1 games
Does not over heat
Since everything is not as compact as the slim PS2, it doesn't have the over heating problem.
No bulky AC adapter
Most of the AC adapter is built into the unit. With the slim PS2, its AC adapter has the large box in the middle, like the Gamecube's.
Playstation 2 slim
Top-loading mechanism
Much cheaper than the ray-loading mechanism, and not nearly as nice. Doesn't represent any form of technology, what so ever. Simple, and cheap. That's it.
Smaller
Because it's smaller, you are getting less PS2 than the original. Why would you want less PS2? Do you hate your PS2? Do you want it to be smaller, so you can hide it easilier? Do you not want to look at it? Why make the unit smaller? I can understand with portables, because larger units are heavier to hold, but you aren't holding consoles. They are left on the floor.
No nice blue "PS2" font on top
Instead, the PS2 slim has a black, shiny strip across the upper portion of the unit, with "PS2" slightly engraved. Doesn't look nearly as attractive. The entire unit is black, with no hint of color anywhere. The blue font really stood out on the original PS2. The slim PS2, is an uglier, smaller PS2. That's it. The beauty has been stripped clean.
Fits on an ordinary, black vertical stand
The slim PS2's black stand isn't nearly as nice as the original PS2's geometric, blue stand, that looks like two 3D right triangles, facing inwards from both sides. The slim PS2's black stand is just a circular piece of plastic that lies horizontally on the floor. Its only purpose is to hold the slim PS2 vertically. It doesn't make the PS2 look any nicer... At all. In fact, it makes it look uglier, kind of like the Wii's vertical stand.
I mean, the Wii is one of the smallest consoles out there (PS2 slim, and a few other consoles, are smaller), so why add more bulk with a gray, vertical stand, with a circular, clear piece, that goes underneath the stand, to prevent the console from falling down, even though it wouldn't, that adds even more bulk?
The original PS2's blue stand, makes the PS2 look much nicer, because the bright blue color, really compliments the blue "PS2" font, and that blue rectangular patch where the USB inserts are. In fact, the original PS2 didn't even need the stand. It could stand by itself. It was mainly for looks, and it did a really good job of it too.
Costs less to manufacture
Because it costs less to manufacture, it might mean that the internal parts are of lesser quality. Like I said, all the beauty, such as the tray-loading mechanism, have been stripped clean, to add a cheaper price, which is not a good thing, because the slim PS2 looks uglier, and has no look of ultimate power... At all... Unlike the original PS2, which really stood out, looks like a powerful console, even though it's weaker than the Gamecube, and Xbox. It towered over many other consoles, when placed vertically. The PS2 slim looks like a wimpy revision, for little 7 year old girls who are too weak to carry the original PS2's box home. It just doesn't represent, or show off, any feel of power at all. It doesn't even look cool. The original PS2, especially on that vertical stand (man, I'm obsessing about that stupid vertical stand. I'll shut up about it), looks a lot cooler than the slim PS2, especially when it's on its ugly stand.
Plays less PS1 games than original
Apparently, there have been a few problems playing some PS1 games on the slim PS2. In fact, there are some PS1 games that wont play on the slim PS2 at all. Some of the PS1 games on the slim PS2 may have more glitches, unreadable text, and other problems, than on the original PS2.
Over heats
Because the slim PS2 is so compact, it has over heating problems.
Bulky AC adapter
Sure the PS2 slim is smaller (which is nothing to brag about, because there's less PS2 to it than the original. It is closer to not existing that the original. It represents less power. At first glance, there is a bigger chance of your eye missing it. It occupies less volume. Et cetera), but it has a bulky AC adapter. I mean, sure I like bigger consoles, because you get more for what you pay for, but nobody likes AC adapters, and all of those other wires. I like to look at my console, not the wires. Therefore, I want a bigger console (not too big. There are limits. And yeah, I'm talking to you Atari 5200, Xbox, and Playstation 3), and less of the cables (which means no ugly, massive box, in the middle of the AC adapter).
These are my personal opinions on both machines. What are yours?