With Conte we wouldn't have made it out of group stage. Remember how we fapped over 4-3-1-2 against Olympiacos as Allegri showed a learning process? There is no such thing with Conte.
When it comes to motivation, tho, Conte is superior. With him we used to destroy all the small teams in Serie A at ease.
Oh yeah, no doubts about that in my mind. Conte is a superior man-manager. Players would run through brick walls for him (in b4 @Martin) and we performed quite a few comebacks as well in Serie A under his tenure. But he really didn't give us a whole lot of confidence before our CL games.
In terms of tactics, something happened to Conte in early 2012. I remember the first 6 months of the 11/12 season, he experimented with 4-4-2, 4-2-3-1, 4-3-3 and then he got the 3-5-2 stuck in his brain (which of course worked in Serie A, but wasn't suited to CL football) and would just refuse to budge and would rarely make any adjustments to it. I remember he used a 4-3-3 against Real Madrid and it worked great. Even though we didn't win either game against them, it was easily the best we played in Europe that season. He'd underrate and talk down about us constantly, and always blabbed on about the high-revenue clubs like Bayern, Barca, Madrid etc. He gave himself (and the team) an excuse to lose before a ball was even kicked in anger.
So far, Allegri hasn't done this once. So in that sense, I think Allegri is better than Conte to deal with European football, he tries to alter things in game tactically and shows a bit more balls to switch things up. It was refreshing to hear him say "we must be at minimum a top 8 team in Europe"
I just hope we manage to negotiate the Dortmund tie (which is going to be extremely difficult) then hope for an "easier" draw in the QF against Monaco or Porto, both whom would be quite beatable IMO.