In order to test the means, you may use a test for testing the normality of your series (ex:with a Kolmogorov-Smirnov test) and the homogeneity of variance (ex: test of Bartlett with alternative with the test of Levene or Brown-Forsythe). For testing the mean of your series if answering normality, use ether the Student's mean test or if your series have not the same length use the Welch test. You may also use ANOVA tests. All these test are parametric. 

Now you may also use non-parametric test which don't suppose any distribution of your series. For instance the Mann-Withney-Wilcoxon test helps you to compare two means or the Wilcoxon ranks sign 's test or several means with the Friedman's test (the only condition is that series need to be continuous). If you have several means of series of different length, you may use the Kruskal-Walis test

If you understand French, you may look at the following adress:

http://marne.u707.jussieu.fr/biostatgv/?module=tests/

Hope this can help you!

G.C.

Usually for old and new, before and after kind of dependent sample problems are taken care by Dependent(also called Paired) Sample t-test if your data is normally distributed. Here is a link to assumptions and other descriptions of paired t-test.

http://www.biostathandbook.com/pairedttest.html

But if distribution of data is not normal Wilcoxon signed rank test is good to go with.

Here is another link to Wilcoxon signed rank test

http://www.biostathandbook.com/wilcoxonsignedrank.html

Good luck

the best way is as followed: suppose that you have time series of both model, for example, rms time series of both for 500 hPa geopotentiel. you first compute time serie of difference.  Now 2 methods are used. First one is bootstrap or similar method, to compute an estimation of difference of rms distribution, and numerically  decide if the actually difference is significant or not (inside a chosen confidence interval). But successive bootstrap samples are correlated, and the result will be hardly corrupted. To have a good result, you must use the correlation correction as presented in Serge Farge paper, derived from Guy Der Megreditchian studies. But SG has proven that this boostrap method is  not efficient. you will have a more rapid and secure result by using student test, provided you decrease freedom degrees as it is presented in SF paper (always derived from GDM theory). Please ask us (SF or myself) if you need concret indication about these methods.