The most similar country to the Czech Republic is, to your surprise, Slovakia. We used to be one state for about sixty years so it we have similar language and many traditions are also alike. We are one country for many foreigners, if they will know where those countries are located. Therefore I focus myself on the main differences.
We differ in religiosity, Slovak people are much more religious, than we Czechs are. It is probably the reason, why try are a bit slightly more family-oriented.
The other difference is, that Slovaks are more willing to move themselves in case of better job opportunity. We Czechs usually prefer to stay within thirty kilometres' radius around the hometown.and then complain about our bad jobs :D.
Also, our currencies differ. We Czechs still use Czech krown, Slovaks use euro.
Next important information is, that our universities are slightly better, so many Slovaks prwfer to study in the Czech Republic. They have an advantage that they are not taken as a foreginers, so can study for free in the Czech Republic.
Last, but not the least, we are a bit richer country, but Slovaks have been improving their standard of living. I think, it will be a same within three or five years.