I just checked the routes on the google maps trip planner and it came up with three routes:
I57 N to I90 E (the Gary route using the Indiana toll road) and it is 446 miles
I74 E to US 24 N to I90 E and it is 437 miles
I 74 E to I70 E to to I71 N and it is 439 miles
Distance wise they are all basically the same. There is construction on the Gary route. I've driven that route a number of times and what others have said about traffic is absolutely true. There is tons of commercial traffic and depending on when you go, there can be a lot of casual traffic as well.
Personally, I would look at the various state department of transportation sites to get an idea on the current construction situation on all the prospective routes and then make the final decision on the weather. I would pay heed to JBord's statement about lake effect snow. But it is not only Lake Erie. The northern route (Gary) gets it as well from Lake Michigan as well. Many times we in the Chicago area will get a couple of inches of snow and Indiana will get a foot or more, specifically east of Gary through to the South Bend area.