Won't be something new. Look at Mass Effect 2, for example. And you forget that ME:Next is a whole new story. It does not have to account for player choices in the trilogy (part of a reason I'm optimistic about it).
I think the handling of ME2's choices in ME3 could've been improved, but at least they tried hard in a situation where they were basically backed into a corner, and most critics and players were fairly satisfied with how the game felt like it responded to their personal story. Mac Walters said when they wrote the Suicide Mission nobody stopped to think how it would affect future games, so I reckon they did their best under the circumstances.
A new galaxy cleverly sidesteps that issue by letting the Milky Way continue on, affected by everything Shepard did in ME3, but giving us a new setting to play in. It's the best solution they could hope for that allows for a game set after ME3 but also one that doesn't disregard the player's canon.
What Shepard did was important but there is no reason for everyone to sing praise to him after 10000 years. Events of the trilogy will be barely mentioned. You might see Shepard memorial and read some codex entries on how Shepard ended the war for your choices to matter. Will be cheap, true, but ditching the entire galaxy to not have to deal with the ending consequences is worse IMO.
I wasn't actually being serious about the 10,000 years thing - that's an insane and terrible idea, even if they're just using it as a weak excuse to get rid of the ending consequences. The Milky Way after 10,000 years would be a far worse option than a new galaxy.
Both of them will be different from Shepard's trilogy, but I reckon a new galaxy with Ark Theory would be closer to what fans are familiar with, at least in terms of the species and conflicts being similar to what we had in the first three games.
After 10,000 years one could argue (in a really stupid way) that "oh the endings wore off", but... everything else would change too. Nothing will be the same as we remember it. All the characters would be dead, civilisations would've risen and fallen many times, there'd probably be dozens of new species, and they'd still be ignoring the consequences of player choices over three games. That is *far* more different than the scenario Ark Theory imagines.
I don't know about most people, but to me a different area of space is less jarring than a different area of time - and they don't need to disregard player canon if they're in a new galaxy.