As someone who's watched Rick Nash play the last four seasons, I see a lot of similarities, but I also see two major differences. Initially I didn't agree with Laine and Nash comparisons, but I think they actually make a lot of sense.
Their skating, puck handling, passing, puck protection, hands are all very similar. Neither are fast, but they get around the ice pretty well, and they have long strides. They won't skate past many players, but their skating is not a liability, and they can get around players from being stronger and craftier than them. They both get their share of 1 on 1 chances with the goalie without having great speed. Both pass the puck well, but are goal scorers before playmakers, so they won't compile many 40 or 50 assist seasons. Both have incredible puck handling for such big players, puck protection where they can control the puck for long stretches of time because of their size, wingspan and strength and both have very good hands around the net, which leads to a lot of goals.
The two main differences are their shots and defensively. Laine has one of the best shots in the world already. He'll score 10-20 goals per season more than most good offensive players who score around 25 goals per season just because of his perimeter shot. Its why I believe he'll be scoring 40-50 goals in his prime. Nash doesn't really have a good perimeter shot. He scores most of his goals close to the net. The other main difference is defensively. Nash is one of the best defensive forwards in the NHL, and while I think Laine has the potential to be an elite defensive forward, I don't think he's there yet. Nash only became really good defensively in the last few seasons, so its something Laine can improve on as he gets more experience, learns how to position himself, how to play certain players, learns how to make high percentage plays, and has a better work ethic defensively.
Rick Nash with one of the top perimeter shots in the league would be a top 5 player in the league. Thats the player that I believe Laine can be. The Ovechkin comparisons are mostly due to his shot and size, but Laine does a lot of things like Nash, and while its easier to compare players to their biggest skill as a player, I think besides their shots and defense, Nash and Laine are really similar players.