The page you mentioned includes a link with more details on the data and methodology used to create this ranking. It's possible to use this to find out a little more about the reasons for the slightly lower rankings of former COMECON countries.
To get started, I made a quick analysis of the data contrasting two groups of countries:
- As a stand-in for “former communist dictatorships”, I used the COMECON members and former Yugoslavian or Soviet Republics that are currently EU members. This list includes the “new members” from the 2004 enlargement minus Malta and Cyprus (those were the original “EU10”), Bulgaria and Romania (EU members since 2007) and Croatia (2013). For simplicity, I called this group “EU10”.
- As a stand-in for “long-time capitalist countries”, I used countries that were members of the EU or EEA before the 2004 enlargement together with Switzerland. I removed Luxembourg and Iceland and Liechtenstein are not even in the original dataset. I called them “EU14“ even though there are more than 14 and not all of them are actually EU members.
The original ranking summarises a bunch of variables, grouped into 6 categories: political variables, economy, environment, gender socioeconomic equality, health, knowledge. As you can see the categories are pretty broad and might not correspond to what you mean by “democracy”, on paper or otherwise.
Here is a graph with a quick overview of the scores in each category:
Going through them one by one:
- There are some differences in the scores on political variables, possibly the ones that are closest to the notion of “on-paper democracy”. I haven't tried to find and analyse the raw data but the variables included are political rights and civil liberties (from Freedom House), gender gap, an index of press freedom, perceived corruption (Transparency International) and recent peaceful change of the head of government and its party. In particular, the differences seem to track Transparency International Corruption Perceptions Index pretty closely. Note that many of these are already complex variables compounding many sources (and ultimately polls of experts).
- Scores for the economy are all over the place but, with a few exceptions (the dot on the far-left with 32.7 is Greece), EU14 countries are at least slightly better.
- On average, EU14 countries might be ever so slightly better on environment variables but it's mostly equivalent.
- Regarding socioeconomic gender equality, EU14 countries are slightly better (probably significantly so if we were to run a statistical test) but the magnitude of the difference is really small and all of them are around 80.
- EU10 countries score lower on health variables, perhaps even more clearly than on political variables. Variables include life expectancy, health expenditure (using PPP exchange rates or as a percentage of GDP), hospital beds, physicians, infant and under-5 mortality rate. Incidentally, the choice to include both outcomes and resources means that countries that get average or even lower outcomes for a much higher cost might actually score better than countries getting the same results without wasting money.
- There are a couple of exceptions and no country with a really good score but EU10 are again lower on knowledge variables. That's school enrolment at various levels, pupil-teacher ratio, telephone lines, internet and mobile phone users, R&D spending, and number of scientific publications per inhabitant.
Without getting in a long discussion of the methodology, differences in ”political variables”, ”economy” and “knowledge” are the most immediate reasons why the countries you mentioned score lower in this particular ranking.
One final caveat: The scores of all the countries considered are between 65 and 85 on a scale designed to go from 0 to 100 (actual range: 35-87) and a dataset mostly restricted to countries considered “free” or “mostly free” by Freedom House. Simplifying a complex issue to crude ranks or categories is in the nature of the exercise but any cut-off is necessarily somewhat arbitrary. There is a world of countries doing much much worse out there so I would be wary of over interpreting the magnitude of the difference.