Osteen is nothing like Finney. Some of Finneys theology was off, but he was a preacher of righteousness, the opposite of Osteens God wants you to be rich and feel good about yourself gospel. Finneys fiery preaching made his unregenerate listeners uncomfortable and led many to repentance.
From my research on Finney, while he had some real theological problems, about 85% of the complaints against him are distortions and exaggerations by certain people who are offended by those who refuse to bow down and kiss the ring of Pope Calvin. Many of these same folks warmly embrace other Calvinist preachers, who preach error more serious than Finneys.
The piece of trash you linked (by normally sound , Phil Johnson) is a prime example. He bashes Finney for sins like not taking the advice of one of his Calvinist mentors and supposedly creating a burnt over region in Western New York, where the gospel just wouldnt work anymore.
Imagine that, a mere mortal was able to turn what Calvinists call the irresistible grace of God into the ineffective grace of God. Apparently, the unconditional election of thousands of previously elect Western New Yorkers was rendered null and void, by Finneys revivals. I cant think of a less Calvinist idea, but some Calvinists abandon all rationality when attacking the heretics who dare question the teachings of Pope Calvin (except for on padeobaptism, which seems to be the one unique area where these Calvinists doubt the infallibility of their Pope.)