I had a 20 US gal tank with loooooooooads of green algae, it grew all over the back wall behind the airstone and all over the sunken ship ornament, it was rather nice and I liked having it there for the fish to snack on. That 20 gal is now empty and my fish live in a 33 gal tank but I only have sparse growths of horrid brown algae. What can I do to encourage green algae?

3 things: SUNLIGHT SUNLIGHT SUNLIGHT!

Once you find a way to introduce more light (especially sunlight) to your tank, you'll get rid of the brown and gets TONS of green.
Brown algae in general thrive in low-light levels. If you can't move the tank to a position where it gets more sunlight, consider getting a lighting fixture that can support more watts.

Nenn is right on-the-money. Once you have brown algae and lots of sunlight, green algae will very quickly take over .

I agree. I have brown algae and that's because my apartment is dark and the tank is not near any window. But, I had to take my plants out of my hospital tank recently for treatment and put them in a bucket out in the sun.... 2 days, that bucket has green algae all over it! SUN, SUN, SUN.

Maybe slightly off-topic, but it just came to me: is it possible that green algae are less aggressive than brown algae towards the plants in a tank? It might of course just be the case that you don't notice green algae very well on a green plant, but I have no idea...

Cheers guys. Well there's absolutely no way I can get my tank to be in more sunlight just yet. Even if it was right in front of the window it would only get direct sunlight for about half an hour each day. I never ever close my curtains but because of the way the houses are (my window is squashed right back between 2 terrace extensions) I hardly get any proper light in my room anyway. Such a shame! I'm all in for giving my goldies for the best and originally I wanted my big tank downstairs in the living room, but my mum said it would make the place look like a tacky Chinese restaurant

I can't afford a new light but I think I could just take the light from the 20 gal tank and add it to the light that is already being used for the 33 gal. I think that might work?

Worth a shot!