I've built about 15 or 20 rifles over the last 40 years ( I make no claim to being good at it: I just like doing it and shooting them) and have done it both ways. I do not like using a router.
It's noisy, and hard to handle even with guides. The last one I built, a .32 half stock, I used a bit and brace to remove a good bit of the channel, then chisels and a home made plane to do the rest. That said, several things are relevant. I'm retired, I enjoy doing things by hand, and I get personal satisfaction in using old hand tools. To each his own.