Generally 2.6 has better hardware capibilties and can use cd-rw drives without scsi enumulation. (Which is one less thing to go wrong). Though it has some problems with older hardware and programs. Yes they should be able to shutdown the PC.
I've noticed that knoppix 3.6 comes with kernels 2.4 and 2.6.
Will both shut my machine off when I close down the OS?
Beyond that what are the pros and cons of each?
Generally 2.6 has better hardware capibilties and can use cd-rw drives without scsi enumulation. (Which is one less thing to go wrong). Though it has some problems with older hardware and programs. Yes they should be able to shutdown the PC.

GIGABYTE B365 HD3 LGA1151 Intel 9th Gen motherboard
$59.99
TUF Gaming Desktop Motherboard - Intel Z790 Chipset - Socket LGA-1700 - ATX
$143.00
ASUS TUF Z390-PRO GAMING LGA1151 DDR4 ATX Motherboard With IO Inlucded
$100.00
ASUS PRIME H410M-K LGA 1200 Intel 10th Gen H410 DDR4 USB3.2 Motherboard M-ATX
$59.99
ASUS H110I-PLUS Motherboard LGA1151 w/ I5-7400 CPU, 8GB, Heatsink & I/O Shield
$60.00
ASUS PRIME Z370-A II LGA 1151 Intel Z370 DDR4 DIMM USB3.1 DVI ATX RGB
$69.99
ASRock B550M Phantom Gaming 4 AM4 AMD B550 SATA 6Gb/s Micro ATX AMD Motherboard
$81.99
Intel H81 Motherboard M.2 NVMe LGA 1150 mATX w/ IO Shield (Random Slot Color)
$29.99
MSI MEG X570 UNIFY Socket AM4, AMD Motherboard
$400.00
ASRock Z370 Pro4 LGA 1151 Z370 HDMI USB 3.1 2 Ultra M.2 DDR4 ATX Motherboard
$75.00