Look at the improvements that the N3DS has over the OG 3DS. Those are my reasons for wanting a new one. Bigger screens without sacrificing too much pixel density, more stable 3D, C-stick, faster loading times, amiibo support etc.
That doesn't really answer the question. Are
you going to
use any of those features? Are you regularly using the 3D on your o3DS right now, and do you think head tracking would substantially improve your experience? Are you playing any games that have C-stick or amiibo support? Do you think amiibos would improve your experience? Do you even own any amiibos? (Have you seen the prices for those things?) Are you bothered by the load times on any of the games you are playing?
I'm guessing my save files will not be carried over? That's why I have to do a system transfer?
What exactly do you think System Transfer does..? Generally, it transfers all internal system data (including the NNID, Miis, and Activity Log data) and the encryption key, so you can just take the SD card out of the old system, put it in the new system, and pick up exactly where you left off.
I think I will just log out of my old 3DS and log in on the new N3DS. That way my old 3DS will not be formatted and I can access my digital games on the new one. Are there any big downsides to this approach?
If you don't do a System Transfer, all your old data is going to be stuck on your old system. I don't know what you think "log out" and "log in" means, as none of your game data is stored on Nintendo's servers (except for maybe Badge Arcade and Pokemon Bank).
Copying save game data without doing a System Transfer generally requires installing CFW on both systems. Technically, you can get around this with some effort, but most people just install CFW.
If you've only purchased a game once and you want to have it installed simultaneously on two different systems, then that would be piracy. In that case you might as well just install CFW on your new system and install illegal downloads from the Internet.