I use statcounter currently, but I have been hearing that analytics is the way to go? Any opinions on this?
Use both. Statcounter is good for small sites, good for the individual tracking of visitors and the real time stats. GA is good for helping you see 'the wood for the trees' and giving you clear views of trends and patterns.
You can get accurate information using Google Analytics + Statcounter both. I'm using it since long time. Google analytics is providing 95 % accurate information while stat counter gives you real time tracking. using both features you can get accurate information of your blog or website at free of cost.
the thing is statcounter will not gonna show the right count if you are heavily loaded with the visitors whereas Analytics seems not to be down
Use AWStats for access logs for exact data. Use Google Analytics for nice visualization of data. StatsCounter is cool but it isn't like having access log programs running on your server for you to view.