First off, DO NOT buy the HD555. It has largely been replaced by the HD598 which can be had for roughly the same price and is considered vastly superior; I will instead be comparing the HD598 with the 280 Pro. I have never listened to the HD598 (although I do own and have extensive listening experience to the 280 Pro) so my comparison of these two are purely speculative.
As you mentioned, the 280 Pro's are a closed design; this means that sound will not leak out which is convenient for use in public places, and it just as importantly doesn't let external sound in! In addition to being closed, the Sennheiser 280 Pro also has some of the best isolation of any headphone I have ever tested... if you are not going to be listening primarily in a dead silent setting, definately go with the 280 Pro over the HD598.
The 280 Pro has better bass and a more linear frequency response up until around 11 KHz, at which point the HD598 takes over in superiority. Since frequencies higher than 10KHz don't add much detail, this translates into the HD598 sounding more open, and having a wider soundstage. However, the 280 Pro will accurately portray a wider selection of instruments. In general, I would say the 280 pro is better for listening to music and the HD598 is better for watching movies and playing video games. Both cans are fairly decent in terms of distortion.
Lastly, the 280 Pro sells for significantly less than does the HD598 ($100 vs $300). As with all full-sized headphones you will need an amplifier; however, both of these cans are fairly easy to drive and can be adequately powered by a $30 cMoy amp.