here we go then
Botrk: +dueling potential, good sustained damage, stronger healing, good vs tanks, high AS
-low base dmg, no wave clear, no defensive stats outside healing
Titanic hydra: +strong waveclear/grants minimal aoe dmg, good splitpush, highest base dmg, health stats, active works on towers
-no AS
Triforce: +best splitpush, good AS, strongest burst, dueling potential, health stats
-low base dmg, waste mana stat, no waveclear
Wit's End: +good vs tanks, mr, high AS, shreds MR for shen mgc dmg, cheap
-no waveclear, no AD, OHE does not apply on towers
Tbh I take either triforce or titanic but you can take any one of the 4. My suggestion is if you take botrk, tri or wits you must have a sunfire cape. Sunfire cape should be essential but deadman's plate is really good on Shen. These items should be your priority depending on the enemy team
Essential: spirit visage, deadman's plate
Waveclear: sunfire cape, titanic hydra
Vs hyper carries/ heavy crits: raduin's omen, thornmail