I think it just depends on the purpose of what you are trying to create. If you are working on something that requires focus on the one subject matter (such as a tattoo design, or character design) then there is really no need to fill up the whole page. In fact, that might be distracting. However if you are working on something that requires an environment, then by all means, fill up the page. You just have to decide what you want to communicate with a given piece. I don't think it is necessary to pick one over the other for the sake of a style Haha, I don't know if that helped at all.
A phoenix is a fire bird, a Rocs is the ice version and a Thunderbird is the (YOU WOULD NEVER GUESS!!!) its... the... ... *dramatic pause* Electric bird... or thunder chicken, but Phoenix can technically be classified to any bird as it translates from its origin to 'Rising bird' meanwhile its English origin translates to 'Dark red' so it can be used in any form. Phoenix also is a way to call someone remarkable in a form of respect.