What is better LVM on RAID or RAID on LVM?

Your current setup is like this:

| / | /var | /usr | /home  |
 --------------------------
|       LVM Volume         |
 --------------------------
|       RAID Volume        |
 --------------------------
| Disk 1 | Disk 2 | Disk 3 | 

It's a much simpler setup with more flexibility. You can use all of the disks in the RAID volume and slice and dice them whatever way you like with LVM. The other way isn't even worth thinking about - it's ridiculously complicated and you lose the benefits of LVM at the filesystem level.

If you tried to RAID LVM volumes, you would be left with a normal device without any of the LVM volume benefits (e.g. growing filesystems etc.)

This is an old question, technology has advanced and the recommended setup is to use built-in RAID support of LVM (see here for setup https://access.redhat.com/documentation/en-US/Red_Hat_Enterprise_Linux/6/html/Logical_Volume_Manager_Administration/raid_volumes.html ), especially if you are using SSD. Red Hat does not recommend the use of RAID 1/5/6/10 with SSD since mdadm will write the complete partition to ensure proper functioning of checksums. This can lead to faster degradation of the SSD, as stated here https://access.redhat.com/documentation/en-US/Red_Hat_Enterprise_Linux/7/html-single/Storage_Administration_Guide/index.html#ssddeploy

Your current setup is fine. This is the recommended way to do it.

Raid deals with keeping the bits secure/redundant/fast/whatever and LVM helps you present them in a esasy to use way.

have hardware raid and you can have lvm on top - best combination.