Sluggish iMac Performance

1) The speed different that you are seeing, is do to the type of internal drive.

The 2013 iMac has a 3.5" 7200rpm HDD

The 2015 iMac has a 2.5" 5400rpm HDD

2) The EtreCheck Pro report, actually shows the drive speed Write 80 MB/s Read 81 MB/s.

Performance:

System Load: 2.28 (1 min ago) 2.35 (5 min ago) 2.69 (15 min ago)

Nominal I/O usage: 2.38 MB/s

File system: 26.45 seconds

Write speed: 80 MB/s

Read speed: 81 MB/s

3) If you want the 2013 or 2015 iMac's to go faster? Consider running from an external ssd.

Use an external SSD as your startup disk … - Apple Community

I also agree with den.thed's assessment. You wrote:

By comparison, I have an older late 2013 iMac.... that runs 110/140 Mbs,

Those speeds are totally consistent with a 3.5-inch 7200rpm, SATA 6GB mech drive as used in higher-end 27-inch iMacs of the time. The "thin-case" redesign of the 2012 and later 21.5-inch models did not leave room for a proper 3.5-inch desktop drive, so the designers used slower 2.5-inch laptop drives instead. Form beat out function, unfortunately.

The ~80MB/sec speeds are as good as it gets for your 2015 model without the external USB3 SSD option. That option should give you ~400MB/sec minimum.

Once you get the external SSD all setup and running you can then abandon the internal HD. The external SSD's capacity should be a minimum the same capacity as your current internal drive's HD. Additional capacity should only be needed if you rely on external HD's for additional storage.

+1 on den.theds assessment!