Great! Thanks for the backstory. By a useful coincidence we have pretty similar hardware in HDD/cpu/RAM/network terms.
With my pool of three vdevs, each 4x4TB RAIDZ1, I get about 900meg/sec large-file read/write speed with caching restricted to a couple of gig - it's faster and more IOPS when I let the cache go to the default of most RAM. So with three vdevs we don't need to worry overmuch about speeds - particularly if your clients aren't also 10gigE, or only one is. 10gigE doesn't practically net you much over 1gigE in general daily usage, and definitely isn't of any benefit for media streaming (until we go to 16K resolutions!) but it is good for doing the replication to a second FreeNAS and other bulk transfers.
As the link I gave explains, you don't gain anything significant by making your vdevs have more disks each, the big changes happen when adding vdevs. So whether to make your new pool out of three vdevs of 5 disks in RAIDZ2 or three vdevs of 6 disks in RAIDZ2 is a cost and capacity decision, not a speed one.
Basically, if you can afford the higher outlay now, go for it.
Consider also that your new vdevs will be much, much larger than the old, and the He10's will also be about twice as fast as the old 3TBs natively due to the head count and data density. You can take advantage of this to reduce upfront costs by building the new pool from two vdevs and add the third vdev later when you have the money and need the capacity and/or extra speed. Or even initially start with one vdev if that has enough capacity, and see whether that is quick enough to support your needs in the short term. You've got the spare slots so you can experiment with that before ordering the second batch of drives.