If you don't have an amp, I don't think any K240 is a likely good solution for you. The new K240s seems to be, by widespread agreement, not very good. The old k240 series are reputed to sound much better, but are all very high impedance, meaning that you'll get very little volume out of them without an amp.
As for whether they're an improvement in sound quality over an SR80, I should be able to tell you in about a week. I have a set of K240 sextets on the way. I have SR80s here, and I like their liveliness, but not their harsh high end and relative lack of bass.
An old pair of K141s got me going down the AKG path. The K240 sextet was recommended to me and with a tip from a fellow forumite, I now have a pair on the way. Hopefully this is the middle ground I've been looking for. I'll post my impressions when they arrive.
If you want to try higher impedance headphones, you could pick up a small amp, like a CMOY or a PA2V2. Both are fairly inexpensive and easily found on eBay.