So I had hoped after going with the BoS I would get a slick paint job at the end, similar to the Institute's all white, but the Sentinel paint job is the same as the Paladin..

The rank on the arm is different, but yeah I know what you mean.

If you're on PC there's mods that should allow you some nicer options.

X-01 Sentinel paint is the one I'm using.

The paint job on Maxson's armor is like that too, if you ever managed to see it.
BoS Elder Rank

When does Elder Maxson wear armor? When we assaulted the Institute he was in his Prydwen flight uniform.

T-60 with the Elder paint. Same as paladin and sentinal just with a different arm marking.

Although I believe his power armor has slightly higher stats than normal.

My question though is where do I find his power armor? Is it in his room?

He has to wear it during the final battle with the BoS. Usually does before you finish the upload of the virus, that and he has a unique Gatling Laser.