If you're taking the train, then one is not substantially any worse than the other in terms of the time/trouble of getting to Shinjuku. As long as your plane's on time and you don't faff around too much upon arrival, you should be able to catch the 9.49pm Skyliner to Nippori, then transfer to JR which will eventually get you to Shinjuku by 11pm. If you miss that Skyliner, though, you'll have to take the commuter-style Access train which will take ~20min longer than Skyliner... but you will still get to Shinjuku by 11.30pm. From HND, you're probably looking at catching a Keikyu train leaving HND ~11.40pm then transfer to JR at Shinagawa, getting you into Shinjuku ~12.30am.
Having said this, some things to consider:
- Airfare difference (obviously)
- NRT flight will get you to Shinjuku earlier in the night.
- If your HND flight runs >30min, you're pretty much out of option train-wise to get to Shinjuku. After that, it's either bus (which doesn't run that often past midnight) or taxi (not cheap).
- The NRT hotel option proposed by AlwaysAisle has + & -. You will most likely save some $ and will get to crash a bit earlier. But the ease of checking into the same hotel as your 2nd & 3rd nights right from the get-go may trump the inconvenience of having to do a round-trip on NRT hotel's shuttle bus and having to unpack and pack an extra one time.