I prefer html5 sites that seem to work flawless in mobile browsers (Chrome, Safari). Apps have more security issues if you are not careful with what the permissions are and who coded them.

Also, if you downloaded an app for everything you access, your mobile would be stuffed full, or of you have endless space you would always be sifting through a sea of semi-useless apps, oh and the "updates"... sheesh! HTML5 developers update and when you revisit the site it is already up to date.