Sounds to me like he's pushing his voice a lot harder to get over the band volume.
In an acoustic situation, he's singing in a more relaxed way, but put all the instruments in, at a volume which is probably unnecessary anyway, and the sing becomes more of a shout.
By turning up his mic a balance will partially be restored, (but his ears will still tell him to sing as loudly as possible), but surely it's better to get that back by turning the instruments down.
Give it a try - there's nothing to lose - except your hearing if that volume is up.
music.stackexchange.com/users/2808/Tim
Craig, the other answers all address the possibility that his "singing nowhere near as good" is because he's getting drowned out by the other band members.
There's another possiblity as well.
If he sings very well by himself, accompanying himself, that doesn't necessarily translate into singing well with other people who are accompanying him.
It's a different skill, and needs to be learned.
You can't be quite as free with the beat if everyone has to stick together.
So if the problem is that he's straining his voice, then yes, you need to work on the mix.
However, if the problem is that everything sounds sloppy, then you all need to work together to get a tighter sound.
I don't mean that he has to get rigid to stay on the beat, that doesn't sound good either.
But there's a kind of tapping into each others ideas that goes on when a band is really playing well together.
Each person has to get to know each other's style, and each person has to value the contribution of every other band member as much as his own.
Sometimes that's a problem for prima-donna type lead singers.
I know this because I've been one myself before. :)
music.stackexchange.com/users/9399/BobRodes
I agree with Tim.
A lot of bands tend to crank up their instruments way too loudly which is unfortunate.
Everybody wants to be heard.
Vocals are crucial for a vocal based band and the band should really work on mixing.
Things you can do are make sure that the Vocalist can be heard clearly over all of the other instruments, especially the lead guitar and drums!
Controlling the sound of drums is difficult especially if there are no mics for the drums.
Band placement plays a role in this case.
However, the volumes of all of the other instruments is totally controllable.
You might also want to consider getting some monitors so that the band members can actually hear themselves.
If you're playing with just the speakers that the audience hears it can be pretty hard to hear yourself clearly.
So my suggestions are monitors and turn the vocalist up and the instruments down!
As I said before, in a vocal based band, the vocals are crucial.
People want to hear and understand the singer.
music.stackexchange.com/users/9131/MrTheBard
"A violin player plays very nice when he is playing by himself.
If he is bowing while another player does the fingering, he's not half as good.
"
"A dancer is dancing the steps of some figure very well by himself.
When he is dancing with another...
" A dancing pair is two beings moving with a common center of gravity and a common purpose.
It takes a lot of practice to arrive there: the end result is one of both doing their part confidently without being hampered by any apparent consideration for the other getting in the away.
In a similar vein, it takes a lot of practice for a band to play as one in a particular configuration.
It will also have taken a lot of time for your singer before his guitar playing and his singing formed one organic unit.
Now he has managed to have the whole performance under his single control.
Which is exactly what is not his job in a band setting.
music.stackexchange.com/users/8773/User8773
Tim's answer coveres the vocal straining
/ hearinign yourself issue, but other factors I have noticed myself : Are the band in tune?
The vocalist doen'st stand a chnace if someone is out of tune with the rest.
Which note should he/
she settle on ?
Which instruments are too loud ?
My band has been using a new bassist for the last year as our usual guy got very ill.
The new fella's bass is a 6 string thingy which goes so low
it makes your buttocks rattle, and on more usual bass notes it's quite all-encompassing, even though not massively loud.
I can hear that I'm singing quite clearly, but it's hard to pick a note out.
A bit of reverb/echo on the vocals helps enormously.
It needs to be in the folback monitors so the vocalist can hear it.
I'm not sure of the science behind that
but it does seem to work.
music.stackexchange.com/users/7337/user2808054
The singer in my band can sing very well. When he is singing by himself playing an acoustic guitar he sounds great. However when put into a situation where he is singing with a full band (ie: studio or rehearsal), his singing is nowhere near as good.  Are there any tricks for him to perform better as a singer when playing with other people?
How to sing better in a band situation?
music.stackexchange.com
<voice><band><rehearsal>
music.stackexchange.com/questions/14959
music.stackexchange.com/users/1379/Craig Curtis
In a band situation, the singer needs to be heard over the instruments or they will be straining their voice in an attempt to be heard. Using a monitor and turning the voice up and the instruments down can usually solve the problem.  It's possible that the vocalist is struggling to be heard. Ways around this would include turning down other instruments or turning down the vocals. Similarly, you could consider getting some monitors so that the vocalist can hear themselves properly.
It's possible that the vocalist is straining to be heard, so you should turn down other instruments or turn up the vocals. You might want to get some monitors so that the vocalist can hear themselves properly.