My question is when outputting movies to dvds and things. Is the quality better when you are using final cut studio rather then just final cut express and idvd. I know that final cut studio comes with final cut pro and another program for making dvds, and compressor. Do these produce better quality movies??

Ultimately, if you know what you are doing, yes.

iDVD uses a Constant Bitrate encoder set to provide 1 hour of footage on a DVD. Compressor allows you to choose multipass VBR (variable bitrate) encoding which is higher quality at a given bit rate.

If you know how to use the tools from beginning to end (camera, capture, codec choice, edit, export, encoding) you SHOULD end up with a significantly better result. If you are flying by the seat of your pants, messing up ANY of the above steps will jeopardize your final output. Be realistic about your ability and knowledge and use the APPROPRIATE tool, which isn't ALWAYS the most expensive.

Btw, the best mpeg2-encoder there is is the Cinema Craft Encoder. It produces far better quality than Compressors mpeg2-encoder. There's a a plugin for FCP, but it's expensive. The cheap "basic"-version exists only for windows, but there's a simple workflow, if you have a Fusion or Parallels:
Output uncompressed QuickTime with Compressor and use that as input for CCE in Windows.
Btw, CCE is really fast, too.