These headphones are tuned exceptionally well. Unfortunately, I have not heard the AKG K371 so I cannot compare them to their sibling cans, but from what I am told, the K371s have a bit more excitement in the bass at the cost of less soundstage.
The K361 is really well-tuned, with accurate tonal balance throughout the whole frequency response. These headphones are also very comfortable, with an all-plastic build that makes for a very lightweight and fatigue-free fit. It's mostly soft-touch plastic that feels rather sturdy in the hand. I imagine most folks could wear these things for hours without any particular problems with comfort.
On The Alan Parsons Project's "Don't Answer Me," the soft background vocals in harmony with the chorus can often fade into the mix on poor headphones. This is especially the case around 2:14 during the lyrics "Run away and hide from everyone." Fortunately, the AKG K361s present the background vocals just fine, separating the vocals well enough to differentiate the background vocalist in the left channel from the lead vocalist in the center and another background vocalist in the mid-right area. It's that mid-right background singer that can often gets buried, but I can pick him out plenty well on the AKG K361.
Transients are also smooth, these drivers certainly run quick enough to make sense of them. On the track "Bremen" by PigPen Theatre Co., vocals have a very gentle reverb on them that can often get buried by the guitar and banjo. The fast decay is audible with these cans, making it easy to track exactly when each note finishes.
Sub bass definitely seems favored over mid bass, with a fairly clear low-end- an exciting but well-balanced bass. I like this pair of headphones for the tune "あめあがりのうた" by Snail's House. I don't consider myself much of a bass-head as I certainly prefer bass quality over bass quantity, and this is one of those tracks than can give me a headache when I play it on bass-heavy headphones. Fortunately, the low-end is present and with plenty of excitement, but tame enough for my ears to really enioy on this track.
As the title suggests, this pair of headphones has one fatal flaw. The biggest problem with the AKG K361s for me would be that it's nigh impossible to get a good seal while wearing glasses. Seriously, the first time I put thes headphones on, I thought something was wrong, they didn't sound right. Then I took my glasses off and they sounded amazing. Looking online, it seems Dekoni Audio makes some pads for the AKG K361/K371 that are alleged to work a lot better for getting a good seal with glasses, but that is adding $50 to a headphone that costs only about twice that. In total one would end up having to pay about $150 total for the headphones and their remedy. I do believe that's still a fair price for what you get, but at that price point one might consider a different pair of headphones instead.
In case you're curious, the headphones come with a fair assortment of goodies, including two cables, one of a short length and one that is longer, as well as a soft tie-up case and a screw-on quarter inch adapter. It's nothing particularly significant, but it's also nice to have the different options for cable length. The cables plug into the headphones with a 2.5mm TRRS end that twists to lock into the left ear. Both cables terminate in 3.5mm single-ended that can be used with the screw-on quarter inch adapter.
The headphones also fold up for compact storage.
Dang, those things look like they've seen some use! I think the arms on my frames are about 2-3mm at their widest, and because the headphones are so compact, anything interrupting the seal in the slightest just makes a world of difference.
One's mileage is sure to vary with the shape and size of their ears and their glasses, but for me it makes all the difference.