Using third party tools to backup
This is just my input, but I have supported most of the major players in the 3rd party backup vendors. I have supported clients that utilize Idera, RedGate, Dell LiteSpeed, NetBackup (which does not really have compression but is 3rd party), and a few off-the-wall vendors that I can't remember anymore.

The improved compression you may or may not get with 3rd party products have a trade-off....CPU workload. I have seen Dell's (LiteSpeed) product run in SQL Server 2014 environment against a database that is right at 500GB, and using high compression kills the CPU. The result was only a backup file of around 64GB. It ended up causing SQL Server to stop providing resources to the backups since Dell's product uses the VDI API. The compression level had to be dropped down from 7 to about 3, this brought the backup size down to about 82GB. We took a native backup with compression enabled of same database, and it was right at 84GB in size. So is the trade off and cost worth it? test, test, test

I seem to recall a client I had a few years ago was using Idera's product and I had constant issues with the backups for their medical databases that were 1TB+ in size. I think some of it had to do with the disk subsystem the backups were being written to, which again is why you need to test. Overall Idera's GUI interface is not inviting to me, and could use great improvement. I would chose RedGate or Dell over Idera any day of the week.

You also have to remember that most 3rd party backup products are going to use the VDI API to SQL Server. This in and of itself can cause problems as well, frequent to often "BackupVirtualDevice" or "BackupIORequest" errors showing up in the error log. I have some of these be false positives (backup actually did occur) and some where legit failures. Make sure to read through the vendor support article or forums. RedGate and Idera have very good support systems in place and are very good about getting back with help. Dell I have not had to make any support calls with their product so far.

The one last thing I will bring up is the format of the backup taken by the 3rd party product. If you get into a DR situation are you going to have a standby server licensed with the product as well? I believe Dell allows you to install LiteSpeed without a license to do a restore, but it has to be licensed to do any backups. I think most of the vendors also include a utility to convert a vendor specific database to a SQL Server native backup file, in case of emergency.