Question: How do I know that my firm is the problem? Will I be happier at another firm, or are they all just basically the same?
Answer: Just as corporations are not all alike, neither are law firms. There are obvious differences in size, practice areas, caliber of work, reputation, etc., and there are not-so-obvious differences when it comes to culture, the way work is assigned, expectations, mentoring and training, just to name a few. When thinking about why you may be less than entirely satisfied with your current situation at a law firm, you should first consider whether it is the firm itself that is the source of your unhappiness in order to be able to answer the question of whether you would be happier at another firm.
If you think the firm itself is the problem, ask yourself what about the firm is problematic. Consider whether the structure, compensation, reputation, people or size bothers you. Talk to friends at peer firms to see if and how their experiences differ from yours.
If you can identify what your firm can realistically do better, and that your target firm is already doing this, than it makes sense to think that by moving you can find what you want and thus stay with your new firm.
Think about your current firm's future, and where you see your future with this firm if you stay. You should think about what you can do to improve your experience at your current firm. If you are convinced that the parameters are such that your experience will not be enhanced by steps you can take there, then think about what firm would enable you to develop a more positive experience.
Objectively evaluate what you appreciate about your current firm. This will enable you to weigh the pros and cons of your current situation more accurately. As we all know, the grass is not always greener.
Take some time to do your research on law firms in the same peer group as yours, as well as ones in different markets in order to more effectively assess how "good" or "bad" you actually have it at your firm. Talk with classmates and colleagues for "insider" viewpoints, and compare those with more objective sources. Consider the fact that it is often a handful or so of people with whom you work on a regular basis that shape your experience at a particular firm, and remember this when asking other people's opinions on certain firms.