..the above app note expalins to you exactly the difference between the series resoannt converter (which you call the LC )...and the LLC resoanant converter.
The above app note is the gospel guide to LLC resoanant converters and tells of the series resonant converter which you speak of.
Of course an LC resonant convertter is just an LLC one with a very high magnetising inductance i suppose.
The series resoant converter sufferes higher frequency variation as load varies....but obviously it can have less circulating current.
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sorry i would correct my spelling but its taking ages for me to re-post after editing..could well be due to my internet connection though.