So I'm taking away from this that grado are better for home use, but dress are better for no sound leakage?
Not exactly.
Basically, all
open headphones are designed for use when you're alone. They leak sound, much like sound would leak out from your window when it's open.
The shell of the headphones themselves actually have openings for the sound to leak out. The people sitting beside you will be able to hear all your music clearly (very annoying for everyone else), and you will hear every conversation happening around you, or traffic noise, car engine.
Closed headphones are designed so that they're not vented, so the headphones are designed to direct the music to the listener's ears (inside the "cup" of each headphone). They will naturally "muffle" all sound around you, since wearing closed headphones is like putting your hands over your ears. In-ear earphones (IEMs) muffle the sound better than closed headphones, but closed cans are much better than open.
The reason why some people like open headphones is because they have what audiophiles call a bigger "soundstage". It basically means that every instrument can be heard distinctly, and it sounds like the music is coming from different areas of a really big concert stage. It's not a big deal for most rock songs, dance, rap, pop, etc. It's when you get to bands that use a lot of rich sounds and instruments where this may be a problem.
In-ear monitors (IEMs) are good because they're very portable, and produce strong bass AND sound isolation. IEMs can easily produce more bass than headphones (closed or open), and so most of them do.
However, they have the lowest soundstage (compared to nearly every pair of headphones), so the music all sounds like it's coming directly into your ear rather than from a bunch of different directions. It may not be a big deal, depending on the type of music you listen to. Personally, I don't think you'd care much.
Also, headphones will always give you high sound quality, even for $50. To get the same sound quality from in-ears, you need to spend at least $100 (or double the money) to match a $50 pair of headphones.
You said you listen to rock/pop/indie, and outside (on a bus), so I'd get closed cans with strong bass ("low frequency"), and also decent treble and clarity, but not necessarily too much. The
Audio-Technica ES7 "Ear-suit" are small and portable like the Dre Solo HD, and look awesome.
Amazon LINK. They're easily driven by something like an iPod or iPhone, unlike some of the larger headphones that may need more power than an iPhone can provide. They're also closed headphones, but small headphones don't generally isolate (muffle external noises) very well, and that includes the Earsuits.
If you don't mind a slightly larger pair of headphones, there are several on the market I could recommend.