Q:

Can't connect to PEAP with wpa_supplicant on Arch

I've been searching around for how to connect to PEAP and there's lot's of info out there, but I can't seem to connect and my University tech support is no help(I'm not really surprised). 
Basically I can connect on my main Arch OS visually with Gnome.   Rowan University's support page shows the setup for Ubuntu and I've been using that to try and get my config right.   This is what they've supplied:

and this is what's in my config file:

The output of wpa_supplicant with -d:

Any help you can give is appreciated and let me know if you need the outputs of any commands. 

A:

I used wpa_passphrase, I had a plaintext password in before and it still wouldn't connect

For PEAP you really must use the password= setting. 
There is no PSK in WPA-Enterprise, and although the password may be hashed for MSCHAPv2, it would use a completely different hash than WPA-Personal PSKs do.  Therefore wpa_passphrase is useless here. 
If it "still wouldn't connect" with a password, then it wouldn't connect for a different reason. 

Are there any bonuses or drawbacks to NetworkManager over wpa_supplicant? 

NetworkManager will just drive wpa_supplicant behind the scenes, and indeed all the parameters you find in the connection profile in /etc are very similar to raw wpa_supplicant config. 
So in your case the advantage is just that you can copy/paste the config, not much more.