They had this really clean high-res, high-poly look and nice colours compared to the more blocky and blurry looking fighting games on the PS2.
I've been messing around with DOA3 and DOA2U on the XEMU emulator and the resolution here is upscaled 3x so what you're seeing is definitely a lot sharper than it would have been on original hardware, but still. Blown up like this it you could tell me this was a PS3 or Xbox 360 game and I'd believe you.
As much as I like the series for its gameplay and as nice as I think the Xbox games look I've always thought that the weakest part of the DOA games has always been their incredibly bland character design and artstyle. Even though they draw from the same pool of martial arts archetypes and stereotypes as every other fighting game series in existence pretty much every character is much more lame and feels less interesting than their equivalents from Tekken, Street Fighter, etc. Kazuya Mishima has more character in his eyebrows than the entire roster of the DOA franchise.
The female cast is supposed to be the draw 
but on balance the designs aren't that much more hornier than most other Japanese fighting game franchises and the characters in those tend to have some personality to go with the fanservice.
One of the reasons I like DOA so much is that compared to Tekken I can actually perform all of the moves in a character's movelist (whether I remember to use all of them is a different thing entirely). I've also been emulating Tekken 4 (my favourite Tekken game, apparently all the competitive types hate it) recently and checking out a character's moves I just immediately give up on a large number of them.
Triangle + X?! Square + Circle?! Neutral inputs?! Four different directional inputs just to do one move?! Go home Namco, you're drunk
Meanwhile I just press different combinations of two buttons in DOA and cool things happen
It's funny that DOA's USP is supposed to be that it's the fighting game series with the sexy ladies. But Tecmo, that's every fighting game series. When SF6 came out my Youtube feed was full of videos of people losing their minds over Chun-Li, Juri and Cammy for weeks
That's like most grappler characters in general. I've heard SNK games can also get pretty goofy with command inputs.
I also loved these stupid DoA games because they were pretty simple fighting games lol. Being able to pull off the single button counter mechanic made me feel like a fighting game pro as a dumb teenager.
Kasumi is literally just Mai Shiranui from KoF in 3d. I think DoA really set the
to the next level by literally making a separate booby bounce sub-engine.
I don't find quarter, half or full circles that difficult, and DOA has a couple of those too. You basically do those in one motion. It's when you need to enter several distinct directional inputs where my thumbs start to short circuit, especially when you throw in a couple of pauses and long presses. Given DOA's stint as an Xbox exclusive from 2001 to 2012 the games would have been unplayable on Xbox pads if they had more complex inputs. Pretty sure I always used the analog stick on the original Xbox
This was really apparent when they added Mai into DOA5 as a guest character. But even then Kasumi's a more boring version of Mai- her stance, the giant pompom thing on her outfit and her paper fans have the sort of visual pop that DOA characters lack