The browser is first-class, there is no better browser on a tablet device period, the drop down menus issues are the fault of lazy developers who assume their work is seen only on desktop machines anymore.
It may be the best in tablets...but I still think (and a lot of others do to) it's a fair experience...pull down menus, check-out experiences, 0 Flash support (whether it's video clips or ads or simply nifty webpage), ability to go to the top of the page by clicking on the top of the tablet but no way for me to go to the bottom of the page with 1 click, etc. I also find the interaction/integration between google.com via the browser and Google Maps app to be terrible. It's too complex to even give a good example on this forum.
iOS web browser needs some help...and/or Apple to push the top 200 websites to become iPad compliant. Both my wife and I have never purchased anything online via our iPad...and I would say we buy online 4-5 times a week at 5 different sites.