Good post TDMM. Here's to a good series.
I'm not going to post who I feel has the advantage; everyone is inherently biased towards their own team. Instead, I'll present my take, hope people read it, and let them come to their own conclusions.
So, in response, a bit of food for thought:
Coaches
When comparing the coaches, it is important to consider the quality of competition, and the quality of their rosters. Specifically Tippett in Phoenix was able to take a rather mediocre roster and turn the team into a playoff threat (in the highly competitive Western Conference and Pacific division). He has done nothing but win everywhere he's gone, and made teams play above the sum of their parts.
Julien has a Stanley Cup on Tippett, but he accomplished this with a much stronger roster than anything Tippett has had access to. Infact, it can be argued his strong teams often underachieved - especially when the chips were down.
For example, Julien was fired heading into the playoffs when he failed to prepare a stacked New Jersey team:
Lou L fired Julien because the veteran Devils players had lost their respect for him. Given how Julien's career went in Boston and what happened to NJ in the 3 seasons afterwards - I donno, maybe coaching wasn't the team's biggest problem?
Also, how exactly was NJ "stacked" after the lockout, yet Tippett's teams in Dallas were "mediocre?" Tippett only coached in Phoenix for 2 seasons; he spent most of his career coaching a very solid Dallas team.
Speaking of underachieving, that very good Dallas Stars team had a 21-26 record in the playoffs under Tippett.
Again, it's not necessarily Tippett's fault they lost, but the idea that Julien's team in NJ was stronger than any team Tippett ever had in Dallas is ridiculous.
Julien gets his teams to play well defensively, but often at the expense of offense. Tippetts system is frustrating to opponents, but allows the players to be effective in all three zones.
Considering Boston had the second best even strength goal differential in the regular season last year (after Vancouver), I'm not concerned.
Julien's teams in Montreal and NJ did regularly finish in the bottom half in offense, but those teams weren't exactly stacked full of good offensive players. Regardless, I'm well aware of Julien's weakness. This line is in the profile I made of him: "Julien was sometimes considered "too defensive" in Montreal and New Jersey and a guy who hurt his own team's offense. I think he learned and became a more rounded coach in Boston."
Despite that criticism, his overall record is no worse than Dave Tippett's record behind the bench. Julien didn't finish 1st, 6th, 7th, 10th, 11th in Jack Adams voting for no reason. True, he wasn't as well-rounded a coach in Montreal and NJ as he's been the last 3 years in Boston. But you know what? If he had been as good his entire career as he is in Boston now, he'd be a decent ATD-calibre coach (especially in a 40 team draft). As is, he's a solid MLD coach, close enough to Dave Tippett in quality where neither team has an advantage at head coach. I mean, I could play the "my guy has a Cup and yours doesn't hahaha" game but I don't feel like it.
Eden Hall's advantage behind the bench lies in John Muckler. Muckler has a lot of experience as either assistant or co-coach of the high flying Oilers. As indicated above, he won 5 Cups in various coaching capacities with the team.
Muckler will handle changing the forwards in-game, while Julien will handle the defensemen. Both men will work on coaching strategies between games.
Goaltenders
When comparing any player through different eras, you need to be aware of the circumstances each player played in. Playoff success in the original 6 was significantly easier to achieve than it was (is) in the modern game. It's a simple game of numbers: 33.3% of NHL goaltenders made the stanley cup final each year in the original six; 16.7% of NHL goaltenders won the cup each year in the O6. When you factor in the greater propensity for dynasties with less teams, a few good playoff runs in a row becomes even more common.
Small correction: There were 7 teams in the league for Mowers' first two trips to the finals.
Anyway, I am well aware of the circumstances. If both goalies had been to the finals once, I would have given the advantage to the goalie in the much larger league, assuming they were both major parts of the run. But that's not the case - Mowers went to the finals 3 straight years, and actually won the whole thing once. Like Lindbergh, he was considered a major reason the team did as well as it did in the playoffs. 3 great playoff performances is significantly more than what Lindbergh did in the playoffs, so much so that it transcends era.
Mowers has the best playoff record of any goalie in this draft, I think. That doesn't necessarily mean that he's going to be the best goalie in the playoffs here. I don't believe in throwing out regular season records for the ATD/MLD playoffs.
But when Mowers already had a slightly better regular season record than Lindbergh, the fact that he is also more accomplished in the playoffs serves to widen the gap between them.
Prior to his time in North America, Lindbergh was strong enough to lead his nation in the 1980 Olympics. Lindbergh needed to overcome the European stigma as one of the first to make the leap to North America. In response to the challenge, he dominated the AHL leaderboard and awards ceremony (AHL First All-Star Team, Harry "Hap" Holmes Memorial Award (fewest goals against - AHL), Dudley "Red" Garrett Memorial Award (Rookie of the Year - AHL), Les Cunningham Award (MVP - AHL) (1981)). His NHL exploits have been discussed already.
More to follow..
Lindbergh was 22 by the time he made his NHL debut and 23 when he became a full-time starter. Mowers was 24 when he made his NHL debut - a normal age for players in the smaller league. I really don't see how Lindbergh was held back by the circumstances compared to Mowers.
Doing well in the AHL in the 1980s when all the best players were in the NHL is pretty meaningless. Johnny Mowers "had a fine amateur career" according to Joe Pelletier for people care about such things.
How important was Lindbergh to Sweden's bronze medal in the 1980 Olympics? It appears that Sweden played 8 games, and Lindbergh saw minutes in 5 of them.
We have the complete Golden Stick voting for the "best player in Europe" for Lindbergh's entire career in Europe before he came to the NHL and he only ranked once - finishing 9th in 79-80. Pretty good but not great. Interestingly enough, Eden Hall's own Marian Stastny finished 8th in Golden Stick voting that season.
(Source) Your guess is as good as mine as to what that adds to Lindbergh's legacy.
But you're not crazy wrong. 
