1. Cost - SPSS is very expensive and has an annual fee. Stata is inexpensive, and is a one-off fee.
2. Easy of use - SPSS is easier to learn, but Stata also has a menu system.
3. Speed - Stata is blindingly fast compared to SPSS
4. Procedures available - SPSS is fine for descriptive statistics, crosstabulations, comparison of means, multiple regression and factor analysis (in other words, simple stuff) - but try running a linear mixed effects model - SPSS is hopeless. If you intend to undertake anything more advanced than multivariable linear regression, Stata is way easier
5. Also consider R - far more difficult to learn and use than SPSS and Stata. As powerful, or possibly more powerful than Stata, but it is free, and like Stata, has hundreds of users around the world writing procedures for it.
Spss is general statistical package while Satat@ is an advanced statistical package
I have been using SPSS for nearly 20 years until I moved via R (about 2004) to Stata (about 2009) - both, as a user and as a teacher. To my experience R is the most difficult to learn and teach (and at the same time the most advanced). SPSS may seem easier to learn for the novice (and easier to teach to the novice). However, in the long run Stata is easier to learn and to teach (and much easier to learn by yourself if you really dare to read the accompanying .pdf-manuals).
If I should summarize in one sentence why I think that Stata is much superior: Since I started to move from SPSS to Stata the ways I look at and analyze my data have much improved - basically stimulated by Stata's consistent GLM (generalized linear model) framework and its associated post-estimation commands. To my mind, to expand your abilities and possibilities is the best a software can do for you.
The ability to use results in (and to automate the use of results for) subsequent analyses is one of the big differences between R and SPSS. In this respect Stata occupies a middle position because it also allows to use results for subsequent analyses (i.e. using post-estimation commands) but with less effort because of its good documentation and the standardization of the output.
The remark that SPSS is usually used in social sciences and Stata is usually used in economics may have been true 10 to 20 years ago, but I doubt whether this still holds, see the statistical consulting web pages of the Institute for Digital Research and Education at the UCLA (https://stats.idre.ucla.edu/). Even if it were still true, in itself this does not tell you anything about the difference between the two packages. Admittedly, economists and psychologists often use a different language to denote the same thing, but this does not imply that it translates into differences in the algorithms and the user interface of both packages. However, in 2009/2010 there has been an attempt by SPSS (i.e. IBM SPSS Statistics) to gain terrain in marketing research and campaigning 'predictive enterprise' (note the attempt to rename SPSS into PASW - predictive analysis software). This may be related to the philosophy that point-and-click were more user friendly than the use of syntax and command files. And it may explain why novices experience SPSS as more easy to use whereas more experienced whould argue that Stata is far more user friendly.
Interestingly, a nearly 20 year old thread about the differences between SPSS and Stata has still valid arguments, although both packages have been much improved, since, see: http://fmwww.bc.edu/GStat/docs/StataVSPSS.html . The best discussion of the differences between SAS, SPSS and Stata (with some remarks about R) can be found in nearly 10 year old report of Michael Mitchell I am attaching to his post (Mitchell_2007.pdf). To my mind the paper is still worth reading (1) because many arguments are still valid, and (2) because of the way Michael delineates the criteria you should use to judge the suitability of a software package for your purposes.
Thanks a lot Nabeel Mahdi Al-Janabi and Dirk Enzmann for your answer.
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