The comparisons below may contain spoilers from Clarke's book (sorry for possible grammatical errors):
- Monoliths, of course. In 3.33 we have Seele and in 2001-3001 we have the Firstborn monoliths. Interestingly, in Q the Seele monoliths are apparently no longer holograms, but apparently a physical device, just like the monoliths in Clarke's novel.
- In both 3.33 and 3001 we have a relevant timeskip.
- Main character recovered and resurrected, both in space and in suspended animation: in 3.33, Shinji is recovered inside Eva01; in 3001, Frank Poole is found frozen.
- The main character needs to adapt to a whole new world: Shinji need to face a post-N3I world with people indifferent to his feelings; Frank Poole needs to deal with cultural shock of a society a thousand years ahead of his time.
- Main character in a strange/futuristic "home": Shinji in AAA-Wunder, Poole in a "space tower".
- Main character faces another (but formerly familiar) location: Shinji is taken to a decadent Nerv/Geofront, Poole goes to an completely different Europa (Jupiter/Lucifer moon).
- A secret in the new location: in 3.33 we have a giant Lilith+Mark.06 fusion and in 3001 a giant monolith.
Huge spoilers of 3001 below:
- In 3.33 Gendo says that Seele (now in physical monoliths) are associated with the flourishing/evolution of mankind. This is said from the very beginning in 2001 (this is the role of the TMA-0 monolith).
- Monoliths "deaths": in 3.33 Seele is "killed" by Gendo (apparently disabling some life support mechanism); in 3001 humans send a virus to the monoliths, which causes them to exhibit erratic behavior and then disappear.
- Both endings have an implicit timeskip, with a battle coming after it: in 3.33 Wille and Nerv will face each other in the future; in 3001, mankind has some hundreds of years before the Firstborn notices the damage in their monoliths.
As said earlier, this may just be coincidence or simply enthusiasm on my part