I was a test admin for a certain storage company that produced tape and hard drive backup products, so I've had a bit of exposure to such things.
Tape drives are slow, yes, but not totally useless. They're good for having an off-site backup. However, cloud storage is a better idea. That's why my old company was going down the tubes so badly. They probably don't have more than a year left for a useful future. They'll probably plug along on old tape revenue from government departments that require Congress's permission to move from it for the next 10 years, without any new products, and then become some savage patent troll company.
Backup to disk products, from single drive USB products to FC VTL products, are the most economical now. They have an up front cost, but cost less in the long run. My personal backups are done to USB hard drives. My current company's backups are done to a RAID 6 set through Linux iSCSI target. (A kind of budget software defined storage setup, with 10.8TB at 10Gb costing us less than $3000)
Cloud storage has it's uses, especially for backups, but there are some major issues with it. It's as slow as your internet connection, which can range from 10Mb effective home broadband to 1Gb business internet. It's still a FAR cry from 10Gb iSCSI or 8Gb FC (which is faster than 10Gb iSCSI due to overhead). Local backups are always going to be faster than cloud. If you're doing backups during the day, then that can interfere with your internet access, as well. In addition, many internet providers do maintenance overnight, when many companies back up. This can cause disconnections (like my current company's backups that get interrupted at 3:00AM every single night) as well as poorer performance even if it doesn't disconnect. If cloud is used for primary storage, avoiding the difficulties of self configured backup systems, the whole company can be brought to a screeching halt by a single construction accident. Cloud has it's place, but that should probably be reduced to just offsite copies of local backups.