Twitter has an API for both languages, so it's probably a matter of which language you prefer to code in. I think python is much easier to write and read than java, so I'd recommend python over java when either can be used. Here's the python twitter api:
Well, I'd too say it depends on he APIs, but maybe not so much on those of Twitter. It depends on what analysis you want to undertake. Social network analysis?
I'm not aware of any good Java tools for this, for python you can use http://igraph.org/python/ (which is also available in R and C/C++). Another great set of tools is http://snap.stanford.edu/ (available for python and C++).
Both are great but i prefer Python(because it's a dynamically typed language, completely based on personal experiences); plus Python has a lot of packages ready to go related to SNA stuff!
Python, especially used with the igraph library, is very convenient to apply existing techniques to your graph, to run basic analysis and extract the information you're searching. So if you only want to do mining, Python is best, because of the iGraph library and the scripting nature of Python (no compilation, no classes, not verbose...).
Now, if you want to design your own network analysis method, something complex (hundreds of lines of codes, several classes...) and/or if your network is very big, then Java can be a good solution. I think Python code becomes quickly messy, but this is personal. But Python is slow, this is not personal, and the iGraph library if slow if you want to design your own processes (iGraph functions are fast, because they are coded in C, but if you manipulate iGRaph objects, it becomes quickly a nightmare)
Both can be used depending on your level of expertise in each language. You can use Twitter API for both languages. I prefer using Python which is much more easier for myself and more productive.
The language to use is up to you but what I can say is that life will be much more easier for you if you use python. There are many python module that can carry out this task for you some of which are is:
BeautifulSoup4 - you can install this by running your command prompt as an administrator, then change directory to where you have you script folder (for example on my own system I will have something like: C:\\Python27\Scripts). You can then 'pip install beautifulsoup4' or 'easy_install beautifulsoup4'. You can then go to there documentation page by searching for it on google and get whatever information you need to collect whatever you need from twitter, you can also check out videos on Youtube.
Scrapy is another tool you can use. Go to github.com and search for 'scrapy' download it and source for tutorials on it. You can also visit the scrapy website.
There are other repositories on github that you can check out by searching with a keyword such as: 'python web crawlers'.
You can also connect to twitter api to get whatever you want by going to app.twitter.com. Then get video tutorials on how to use it with python.