I ride a Trek 8000 MTB from about 15 years ago as my commuter. This is a rigid fork bike. The only modification I made to the original was to replace the knobby tires with slicks. When the bike was new I had put a baby carrier on the rear that came with a Blackburn rack as part of the system. The rack is still there, the baby is now 17 and taller than I am. He also has adopted one of my bikes as his own.

My commute is 10 miles of Brooklyn and Manhattan riding on rural country roads - NOT. Actually it is 10 miles almost entirely on bike lanes, just the first few blocks in my very quiet neighborhood and the last 8 blocks in midtown Manhattan. The half upright position is perfect for the kind of riding it is. Weight only matters if you can't lift it. On a commuter with your stuff it'll weigh a lot anyway. I carry a laptop and clothes and whatever else I need, but no chain and lock. I keep the chain tied to the pole outside my office and have a U-Lock at home for when I want to lock up the bike otherwise.

Changing out the fork on your Trek is probably not something you were considering. The Raleigh is probably a better choice from that standpoint, but at least put decent lightweight slick tires on whichever you use. Leave the knobbies for the trails.

10 miles will seem like a long ride the first time you do it. Do it a few times on the weekend before you commit. Since you have both bikes, try it on each. It'll feel like nothing after the 3rd or 4th ride (unless there's a killer hill, then it will always be a killer hill)