Well, the upside from a convenience standpoint on a Android is that info in your Google Accounts is physically separate from your old phone, and will be there for your new phone too.  If you use Google Music, for example, all of your music will be in the cloud.  I guess that is true of Apple's products too, just a different universe with iTunes.  Much of your data such as music, pictures, etc., are probably already stored on your existing phone's SD card, which should be a simple switch out, or you can copy the data if you prefer.  If you do want to copy it, the easiest and safest way is probably to use Dropbox to make backups.  You should be able to Google Play and push all your apps into your new phone.      

Assuming that your phone isn't rooted, there is an easy way to take care of it, all for the low, low price of $4.99 plus tax.  MyBackup Pro will pretty much do it for you.  Install it on both your old and new Android, and the app will guide you through the process of moving things over and/or backing up your data on the company's servers.  You get everything done on your old device, then go over to your new one and choose to restore apps and media, and the app should do the rest.  Repeat for data and that should do it.  If you phone is rooted, there is a version of MyBackup for that, but I have never tried it.  

The process should be pretty easy.  I would spend the $5 myself, but it isn't absolutely necessary.