Most importantly, do whatever works for you.
If you can fit your daybag into your main backpack for those in-transit days, then definitely do it. Less is more. One less bag to keep up with, two hands for handling train tickets, food and drinks, holding handrails and poles/straps in the metro/bus.
But if you're like me ;-) that isn't usually the case. I carry my main backpack on my back, then usually hand carry my other bag (usually a Civita Backpack or something similar; most smaller backpacks have a hanging strap at the top for hand-carrying, or just use one of the straps). I sometimes put one day bag strap over or under one of my backpack straps and carry it on my shoulder (like a purse). Depending on the two backpacks, it can be difficult getting the smaller bag's strap to stay on the larger bag's strap. Or, wear your smaller backpack on your frontside - just put your arms through the straps and wear it on your chest/tummy, either under or over your larger bag. Trust me, you won't be the only person you'll see doing this.
FWIW, I have probably worn my day bag backpack on my back for about 1 hour total in accumulated minutes over many years. I wear it slung over one shoulder like I wear my regular purse.
With all of the crap stuff I've been known to carry in my main backpack, I'd have some serious shoulder and back issues if I carried it on my shoulder with a shoulder strap for longer than a few minutes here and there, so I applaud you for (apparently) not having a terribly heavy carry-on bag!
And however you carry them, take them off on metro cars, buses, and boats.