svenska storstaten = the Swedish Empire
http://en.wikipedia.org/wiki/Swedish_Empire

Erikarnas Stor-Sverige = the Great Swedish Power of the XXX
The XXX would depend on which "Erics" you mean, historically.
Cf. e.g.:
http://sv.wikipedia.org/wiki/Erik_XIV
http://en.wikipedia.org/wiki/House_of_Eric
(I suspect you mean Erik XIV and his descendants - would that make sense, anyone?)

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Note added at 19 mins (2013-12-26 18:16:46 GMT)
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Actually, on a second thought, there is an ambiguity... "Storstaten" could refer to:
- a state that is big in terms of territorial conquests, an Empire;
- a state that has risen to great heights in another sense.
I suspect your author is more referring to the latter. In that case:
svenska storstaten = the Great Swedish Power or the Great Power of Sweden

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Note added at 2 hrs (2013-12-26 20:09:23 GMT)
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Or, if I'm right about my interpretation, why not just:
svenska storstaten = the great Swedish state
Erikarnas Stor-Sverige = the great Swedish power of the XXX

In parallel wit 'Greater Israel' which we translate with 'Stor-Israel:
The 'Eriks Greater Sweden'