There now follows a brief explanation of the differences and similarities between the American term for waste, and the British, because they’re not the same, and the words don’t carry the same resonances when used in other contexts.
Don’t worry though, I will be coming to a judgment about which is the better one, just so we’re all clear.
Let’s start with the basics: in America the object with the plastic bag inside, into which everyone puts things they no longer want (and cannot recycle or churn up in the waste-disposal) is called a garbage can, or garbage pail, or trash can. In Britain it’s called a rubbish bin, or just the bin. Americans would say “throw it in the trash,” and we’d say “throw it in the bin” and that’s that. Rubbish is what is placed in the bin, just as garbage goes in the trash.
Rubbish and trashy are also adjectives, but they have very different meanings. If you call someone (or something) trashy, you’re saying they’re a little morally loose, or cheap, or keener on style than substance. You might be calling their integrity into question, but there can also be an undercurrent of temporary admiration, of the sort you’d normally reserve for a sole firework. If you say someone or something is rubbish, you’re saying they’re inept or unsatisfactory. There’s no positive undercurrent, no brash empowerment. It’s a mild word, and can be said with affection, but it’s never a compliment.
For example, depending on how you feel about their music, you could say the Spice Girls were (or were not) rubbish, but they were firmly, defiantly trashy at all times.*
Both words have also served time as verbs, with trash being a word for destroying something so that it becomes worthless and rubbish being used to mean the same as discredit.
So Keith Moon of the Who could be said to have trashed many a hotel suite. but his closest friends have all rubbished the story he often told about driving a Rolls Royce into a swimming pool.
Ultimately though, trash has to be the winner, for sheer Swiss Army Knife usefulness. You can use it to tell a whole story: get trashed, trash the place, trashily, pick up the trash, put the trash in the trash, take out the trash, get trashed (again).
Take it away, (the London) Suede!
* The New York Dolls even managed the feat of being trashy, and technically a bit rubbish too, without ever being garbage.