Even if you don't count that HoH, Steve still won more competitions than Liz.
I mean Vanessa had her fooled about taking her to F2. Liz didn't know how great of a game Vanessa had played, she even admitted it afterwards in interviews, and she was stunned that Steve took her. After she was eliminated from the final HoH, Liz never even talked to Steve about bringing her instead of Vanessa, and I think that shows she really would have taken Vanessa had she won, and she would have lost in a landslide against Vanessa but I think she had at least a chance against Steve. The fact that she never even prepared arguments or a speech against Steve is just embarrassing for her, especially when she had so much downtime and with so much on the line ($500k).
I think we'll have to agree to disagree, but I do think Liz and Steve are comparable as far as their player skill goes, but I think Steve deserved the win for having the perception and strategic knowledge to evict Vanessa, the best player of that season.