You will partly drain Lake Superior into Kraken Mare. Until the ice mound plugs the portal.
The atmospheric pressure on Titan is 150% that of Earth.
https://en.wikipedia.org/wiki/Atmosphere_of_Titan
The surface pressure is about 50% higher than on Earth at 1.5 bars
(147 kPa)[1] which is near the triple point of methane and allows
there to be gaseous methane in the atmosphere and liquid methane on
the surface...
The two lakes are comparably deep (400 m). Liquid methane is 65% the density of water. The pressure at 200m of water is about 20 bars and so the pressure at 200m of methane is 13bars. 20 bars for depth + 1 for atmosphere = pressure of 21 bar on Earth side. 13 + 1.5 = 14.5 on Titan side.
Pressure is higher on the Earth side so water will leave Lake Superior and flow to Titan. Ice is denser than liquid methane so it will sink into the methane lake. The methane lake will boil because of the heat of incoming water. As Superior drains, the pressure of overlying water will decrease but the overlying methane pressure is decreasing too as it boils away. Kraken Mare is much bigger than Superior and so I think the level will change less there.
Flow will stop when pressure has equilibrated. I figure that will be when the level of Superior has dropped 132 meters.
It will stop before then if enough ice has piled up around the portal on the Titan side to occlude the portal on that side. This might happen long before Superior drops appreciably. If the ice piles as a cone, a cone 200 meters high and 200 meters diameter has a volume of about 2 million cubic meters or 2 billion liters. The Great Lakes contain 22 quadrillion liters. 2 billion is a drop in the bucket.
Climactic changes on Earth will be those that result from a very slightly smaller Great Lakes.
Climactic changes on Titan will be rain as methane boiled off the lake condenses and rains back down.
Investors in an awesome portal between worlds might be disappointed.