I plan to travel from Dalian to Harbin, may i seek advise on which way is better?

You are suggested to follow the first route, since there are three trains from Shengyang to Baihe (the nearest station to the mountain), but only one from Jilin.
BTW, the three trains leave at 9:11, 18:54, and 20:18, which take 13h -13h 30 minutes, and CNY158/152 for a hard sleeper, CNY243/ 233 for a soft one.
After getting to Baihe, you can hire a private car to the mountain with a fare of about CNY150 for a round trip to the North Slope.

Thank you Steve for the useful advise. The following is my 15 days itineraries , appreciate it if you can advise further on the viable, thank you.
Day 1. Dalian
Day 2. Dalian
Day 3. Dalian to Dandong, take evening train to Shenyang
Day 4 take 17:05 train from Shenyang to Baihe
Day 5. Visit Changbaishan north slope
Day 6 Visit Changbaishan west slope
Day 7. Changbaishan to Jilin
Day 8 Jilin
Day 9 Jilin
Day 10 Jilin to Snow town
Day 11 Snow town
Day 12 Snowtown to Harbin
Day 13 Harbin
Day 14 Harbin
Day 15 going home

There may be some problems, and I’d like to give you suggestion.
The train from Baihe (Changbaishan) to Jilin leaves at 6:38, so you need to take it in the early morning.

It’s hard to snow town from Jilin, actuall, you can go to Harbin first and then to the snow town.
Harbin - snow town : take a train to Yabuli and then hire a car there. The car costs around CNY500, but you can share it with other visitors.