Hard for me to comment honestly on sound as my Ultrasone HFI 780 were sent to S2 Audio by their previous owner and had internal damping changed so probably sound a bit different.
1) Portability. Must be able to fold or be easily stored.
Both are equally portable.
2) Requires no amp to sound good. (Will be used on a laptop/mp3)
Sorry but this is a pet peeve of mine - no headphone can be used without an amp. Your lap top has one inside, and so does your mp3 player. You mean does not require excess amping. Sorry I know that sounds petty but I really want people on head-fi to stop using the term "un-amped" it drives me mad. With that rant over -
Some will tell you overwise, but I owned the M50 for well over a year and tried it with numerous amps and devices and IMHO the M50 can be powered to its full potential by any amp and does not really seem to "scale" in quality with better quality amps, it sounds basically the same through an MP3 player and a beefy desktop amp. The HFI-780 will have its power requirements met by the amp in an MP3 player but undeniably does "scale" - so will sound better with a better quality amp.
3) Closed-back for isolation.
Both meet the criteria. I think the HFI-780 stock pads are better for isolation. I say this as I got them worn out already - and they isolate extremely well. When the M50 pads are brand new they isolate like a dream but that ability drops as they compress and get older. Still, they both isolate, but with the M50 buying new pads once or twice a year is advised.
4) Circumaural (around-ear) as opposed to on-top-of-ear.
Both are but how big are your ears? I say this because the stock HFI-780 pads don't give you a lot of room compared to the M50s. I have pretty big ears and have to find exactly the right position for it to be comfortable, the M50 pads are softer, give more space and are a lot more comfortable. I am actually going to try working out how to make the M50 pads work with the 780 (they fit, I have them on now) but the bass loses some tightness and mids recess. In my experience blocking the vents should sort that out… Another option is to try DT250 pads, but they suck for isolation.
5) Good BASS. I currently own a pair of MDR-7506 and they have very accurate bass reproduction, but I sort of want something that has much more bass presence.
Again, with the disclaimer that my HFI-780 have been damped - I find the bass to be two equal flavours rather than one being clearly superior over the other. To my personal tatses, maybe the 780 just clinches it, but there is no knocking the M50 bass. I would rate them thus -
Soundstage - Draw, neither particuarly impressive
Bass - Draw, comes down to personal taste, Ultrasone is a little punchier and faster and greater in amount, M50 a little warmer and more textured. I'd really like the 780 bass quality and the M50 bass quantity.
Midrange - M50 wins. Ultrasone midrange might be nice but is clearly not the star of the show with bass and treble crowding it out. Slight metalic "closed" sound on the Ultrasone too, none of which the M50 suffers from.
Treble - HFI-780 wins - much more sprakle and energy and is surprisingly open sounding for a
closed phone. The M50 does suffer from the "metalic" closed sound with the treble.
Overall - It's a "matter of taste" thing rather than a case of one being better than the other. I haven't made my mind up yet as I've only had the 780 for a week or so.