Your phone probably is
a more powerful computer than the eee pc 701. What is your goal for this outdated hardware? In other words, what applications do you hope to run? What tasks do you hope to accomplish?
The first step toward getting answers is to tell us which distribution ("distro" for short) is installed on your eee. If it's the distro that came preinstalled on your eee, called "Xandros," it is obsolete and outdated, which is why you can't update Firefox or anything else. Basically not recommended.
So if you wish to have a happy Linux experience on your eee, you'll need to replace Xandros (if that is what you have, I can't tell from where I'm sitting
) and do a fresh reinstall of a currently-supported "lightweight" distribution that supports old hardware. Some of the more popular lightweight distros include: AntiX, CrunchBang, Puppy, SliTaz, Tiny Core, etc. (this is a very
frequently-asked topic on these forums; just do a Search on "lightweight" and you'll get all sorts of great suggestions). I suggest you visit the websites for these lightweight distros, search their forums, see if any users have reported success on the eee pc 701, and if you are comfortable with the friendliness and knowledgability of the people on these forums to support you in this task.