Jordan really came all guns blazing into Dream Theater. SFAM was a great introduction leaving no doubt that it was the right call to bring him on board. He had a great lead tone and made good use of it with melodic & memorable solos such as Fatal Tragedy, Beyond this Life, Home. He even had the inspiration to make something truly iconic, the ragtime solo in TDOE.
He continued red hot on Six Degrees, Blind Faith being a standout performance (both the piano & organ solos are lovely).
However, Train of Thought was a misstep in my opinion. The band going for an overly heavy sound squeezed him into a tight corner. Much like Jon Lord on Machine Head, he went for a heavy guitar-like sound, but unlike Jon's Hammond tone that still managed to sound good and unique, Jordan's guitar-like, wah-wah drenched lead sound really cannot be justified. It just sounds like a bad guitar. The first part of his Budokan solo is probably his worst Dream Theater-moment. The wonderful second part redeemed it somewhat though.
(edit: It's funny, I haven't been on DTF for ages and just checked out my post history. My second post ever, nearly from a decade ago, is basically the same thing, me trashing JR's Budokan solo, but mentioning the redeeming qualities of the second part.

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After Live at Budokan came out, my piano teacher gave the DVD to me, suggesting to pay attention to Jordan Rudess, 'cause he's one of the greatest. Being an avid classic prog rock enthusiast, I remember how disappointed I was after the first two songs, so I decided to fast forward to Jordan's solo, which was even worse. I remember saying to myself: what's the point of a keyboard solo, if he makes it sound exactly like an electric guitar? Fortunately, the second part of the solo was better and after that I checked out Instrumedley which completely blew me away and prompted me to check out their discography. I&W and Scenes became instant favorites because of Instrumedley and since then I came to appreciate all their albums, including ToT.
After that, he thankfully went for a classic, tried-and-true analog keyboard sound, with a fabulous, melodic solo to match: the Moog solo on Octavarium, which is arguably his finest hour.
Since then, his playing has settled into a predictable, comfortable pattern, no big standout moments, some "wanky" parts, but overall he's solid and enjoyable all around. ADTOE is his strongest showing in the Mangini-era, but I'm quickly worming up to the latest album as well.