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.

SK Hynix 1TB PC801 M.2 NVMe PCIe Gen4x4 2280 SSD
$100.00
Samsung 2.5" 870 EVO SSD SATA III 250GB 500GB 1TB Internet Solid State Drive Lot
$60.00
External SSD 1TB 2TB 4TB Portable Hard Drive USB 3.0 Type-C High Speed PC Mac
$19.99
Dell Latitude 14" Laptop Computer Intel i5 Up To 32GB RAM 1TB SSD Windows 11 Pro
$545.25
1TB Kingston DataTraveler Max DTMAX/1TB USB Type-C Flash Drive
$86.95
Crucial MX500 1TB 2.5" SATA III Internal SSD CT1000MX500SSD1
$99.99
SAMSUNG T7 Portable SSD 1TB Indigo Blue USB 3.2 Gen2 External MU-PC1T0H/AM
$159.99
Acer Predator Helios Neo 16S AI 16" i9 275HX 2S RTX 5070 Ti 32GB 1TB SSD Refurb
$1746.47
Dell Latitude 14" Laptop Computer Intel i7 Up To 32GB RAM 1TB SSD Windows 11 Pro
$330.73
External Solid State Drive USB 3.2 Gen2, 1TB SSD External Hard Drive with C to A
$100.00