If your new stats program is a log-based application and isn't excluding spiders & bots, I wouldn't be surprised to see huge differences.
Bottom line, no analytics program is going to give you exactly the same numbers as any other. The important bit is not the precise numbers of visitors you get, but the trends and the paths they take through your site.
If you like your new stats program, use it. If you prefer Google Analytics' interface, use that. Either one is going to be better than not using an analytics package at all.