Miller. He brings shooting, rebounding and OK defense, and probably good defense in the team' schemes.
Shaq only brings a presence in the post but he is a liability defensively and he might cause chemistry issues, not to mention he is too old, so no, thanks, I'd take Miller in a heartbeat.
I'm a Shaq guy myself. Even at this stage of his career, you must account for him or he'll make you pay. He best asset is getting the opposing team in foul trouble early and often. Something the Celtics could use dearly, since Pierce is the only one who gets to the line nowadays. He remains a load inside. Brad Miller shooting is overrated, he shot the 3-ball way worse than Sheed (28%). And he isn't as good of rebounder as Shaq. Defensively both of them need help, that's why Perk coming back helps the team in that department.
I agree that Shaq's offensive game is still unstoppable and that's what I acknowledged it as his asset. But, to me, that's his only asset. Sure, he can score down lown and put the other team in foul trouble but, on the other end, he just opens up easy ways for the opponent in the lane when they play pick & roll or simply throw a quick PG or guard in the paint. Shaq can only play D one on one at this stage of his career so he is a big liability for the team's defense. He is too slow to react in time to pick & roll and other stuff. Re-watch some highlights from Rose and Rondo during these playoffs and you will see how terrible he was (starting with Mo Williams' atrocious D of course, but still

).
As for his rebounding it's not so good in my opinion, he still has a size and weight advantage but that's it, Miller wouldn't do better but not really worse.
As for Miller's poor shooting percentage last year, let's not forget almost all his attempts came from the perimeter and he was kind of asked to replace Ben Gordon's spacing so it's kind of a moot point (like Sheed's career low in 3 point % this year because he attempt A LOT of them during the season, but shot better in the playoffs and took less attempts).
Anyway, my point is, I wouldn't spend a chunk of the MLE on either of these guys but if we could bring one of them with the veteran minimum I would take Miller. And if we really HAD to use some part of the MLE I would use it on Miller.