Is it equally effective to backup my apps, photos, contacts, SMS texts etc on my Android Smartphone (which is non rooted) using MS Skydrive or Dropbox compared with using a dedicated Backup App from the Google Play Store eg My Back Up Pro ? Is it the case that, it is as effective but the process is far simpler and less time consuming to carry out if a dedicated application is used. This applies to general backing up and backing up in order to migrate/transition as seemlessly as possible when upgrading to a new smartphone
You would have to look at the pros and cons.
Pros of Cloud Backup
Cons of Cloud Backup
Pros of Dedicated Backup App
Cons of Dedicated Backup App
You also have to bear in mind that My Backup Pro (which you mentioned), has the ability to back up to the cloud as well as file backups. You can also set scheduled backups.
With this in mind, I would say that a Dedicated Backup App would actually be better and easier than using a standard cloud service.
One more thing to keep in mind is privacy: While you mostly have control over your locally stored data, you cannot say the same for Cloud services. For storing personal/sensitive information to the Cloud, you should always consider encryption.
A third option is to have your app creating backups on your sd card, and use another app (e.g. FolderSync) automatically sync the backup directory to your local computer (or NAS device). This way you are a bit safer if your card breaks, and have more privacy. And you have both, a local and a remote backup -- plus even if you need the latter one, download is a bit faster as from the Cloud. If you trust some Cloud service, chances are also good that service is supported by FolderSync as well.