Both sulfuric and nitric acids are NEUTRAL species. Lewis dot formulae should (and do) reflect this neutrality.
Typically, we would display the sulfur in sulfuric acid as a neutral species, with 2 ##S=O## bonds. Thus, we would get the Lewis structure: ##(HO)S(=O)_2(OH)##. Alternatively, we could represent charge separation: ##(HO)S^(2+)(-O^(-))_2(OH)##, which is arguably a better representation.
On the other hand, nitric acid MUST display a quaternized nitrogen (i.e. formally positive), and a formally negative oxygen charge: ##HO-N^+(=O)O^-##.
All of these Lewis structures are representations of actual NEUTRAL and ISOLABLE molecules. The Lewis structures that I have tried to represent are conceptual, and may or may not represent chemical reality.
Neither Lewis representation will indicate how or why sulfuric acid is a stronger acid than nitric acid. This is an experimental phenomenon, and is not dependent our Lewis representations. In fact, sulfuric acid is a stronger acid than nitric acid, and will protonate nitric acid to give the ##NO_2^+## cation:
##H_2SO_4 + HNO_3 rarr NO_2^+ + HSO_4^(-) + H_2O##
I’ve forgotten what you call the ##NO_2^+## cation! It might come to me presently. Ah, it’s the nitronium ion.
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