Since you already have an AKG, I'd recommend the MS1 for a complete change in sound signature (assuming you'd be ok with its forward and aggressive nature), but not without reservations. I agree with the many on here who think the MS1 is the best phone you can get for $100 new, but (as long as the 240S is being amped) I love both of these phones. When the K240 is well powered, I think their performance is at a pretty similar level, but the MS1s forward presentation makes them more immediately impressive (especially to inexperienced listeners, I've found). The MS1 has the added benefit of sounding good out of anything, the K240 has a tendency to get a little muddy in the low end when used unamped for bass heavy music. I think both are very fun and engaging phones, with the edge going to the MS1 for its more crisp, impactful, and aggressive nature.
Both have a very nice midrange. K240s highs are rolled off a bit, MS1s are fairly pronounced. Both are pretty strong in the low end, but the additional impact of the Alessandro usually makes it more impressive, at least for rock. I find the K240 very comfortable, but the cups don't have as much room as your K501 so your ears might touch the cloth over the drivers gently. The pleather, which is also of good quality and very soft, can induce a little sweating. The MS1, like any Grado, has some comfort issues, but since I gave the headband a good bend a couple weeks ago I find its comfortable for hours even with bowl pads, probably a very individual thing. One area where the K240 clearly excels is in its soundstaging. It doesn't have the width of the 501, but I think it does have a nice depth to it and I've found that it seems to position sounds better than most of my other phones. The MS1s soundstage is very compressed and in your face, little width and less depth, everything just right there in your head. The only real weakness I've noticed in the 240S is a tendency emphasize sibilance in some closely miked female vocals, despite the gentle and rolled off nature of its treble. It's been suggested by some that the sibilance tends to go away as the pads flatten and as the phones burn in, but I still notice it in mine after probably a year of ownership.
Of course if build quality is a concern to you, there's no comparison. The Alessandro will seem very cheap next to your K501, with it's rough-edged vinyl headband and cheaply-molded plastic. The K240 is beautifully made with a leathery looking vinyl headband and high quality plastic, and the golden rings on the sides are milled from a brassy metal.
As long as you have enough power, I don't think you'd go far wrong with either phone. To comment on the musical styles mentioned in your profile: Both are good with acoustic music (solo guitar, folk, etc), MS1 a little better due to how well its intimate sound works with that kind of thing. I tried the K240 with classical a while back and thought it did pretty well considering its fairly small soundstage, the MS1 can sound gorgeous with solo violin but doesn't really have the soundstage to do symphonic stuff justice. Of course neither of these are considered classical phones. Both are good for jazz, I can't say which I prefer since I haven't listened to enough to compare, but I believe I have found the 240S's sibilance to be a problem on some (probably poorly recorded) horns. For rock, most would probably prefer the forward, impactful MS1, but they're both good and I'd say it comes down to taste.
As a disclaimer, I've been listening to my MS1 almost exclusively for the past few days and haven't listened to the K240 very much since I got the K271 a couple months ago (also a very nice AKG), so I might be in a Grado-biased phase right now. Though I did do a quick comparison of the 240 and MS1 to check my recollection of soundstage differences while writing this and I've been listening to the 240 since, reminded me how much I like this can for its fun but somewhat relaxed sound. Also, my MS1 experience is almost entirely with modified Sennheiser pads, bowls, and reversed bowls, not the comfies it comes with. So with all that in mind, these are just my opinions, remember the usual grain of salt that should always be applied to any opinion around here.
Hope my rambling helps in some way, I've heard it said that not many here own both of these phones so I figured I should chime in with a response. If you haven't already, do a search and you can find a ton of information on both of these.
