New Shen is absolutely terrible.

Shen has no way to farm safety: While it can be argued that Shen's Spirit's Refuge (his W) can help him farm by preventing him from being hit by auto-attacks, it can only be used once every 18 seconds and only blocks attacks for 1.75 seconds. In order to do this, however, he also needs to expend his Q to move the blade, which gives him his boost in damage which he then has to use on minions instead of hitting his opponents. Shadow Dash costs 100 energy, so if Shen wants to get in, CS, and get out without being punished for it, he's using 380 energy, so thank god he has 400 energy. That of course, however, means that if Shen tries to deal damage to his opponent before trying to CS, he won't be able to get out without taking a lot of damage. Add on to the fact that Shen's W doesn't block spells and Shen enters an even more sad place. His laning is worse than it ever was, and he has no ranged abilities. The only way he can deal damage is by auto-attacking someone with his Q up or landing a taunt. Because of Shadow Dash's extremely long cooldown, if Shen doesn't have tons of movement speed, he'll never be able to run away from or catch up to an opponent. He won't be able to throw Vorpal Blade at an enemy to help. If he misses his taunt, he's a useless sitting duck for the rest of the teamfight.

The only thing that is keeping Shen even remotely playable at the moment is his ultimate. If Riot wanted a champion that you pick so you can press R, Shen is the posterboy for that, because he sure as hell isn't doing anything else for the remainder of the game. Shen has no lane presence, no teamfight presence, very little split push presence, so the only thing he's got going for him is his global map presence. Shen needs some way to deal damage at range, or at the very least, he needs to have better base or scaling stats so he doesn't get walked all over by anyone he comes to fight against.