Notes works on iCloud on both devices. Make sure they're both turned on (in Settings > iCloud) and they both use the identical Apple ID and password.
They'll never be exactly the same because your iPhone and iPad may well have different application data that does not get synched. For example, if you use Shazam, both will have different songs that you might have found.
You can make sure both have the same apps by going to Settings > iTunes & App Stores and turn on automatic downloads for all three categories.