The bus is probably easier, yes If you love trains, you can still take one from Nazare to Porto, but it will involve a few changes. You'd need to get a local bus or taxi to nearby Valado and take the train on from there. Travel time probably isn't much more than a bus just with changes. The direct bus is of course much simpler, but some of us don't care for long bus rides.
The bus station in Coimbra is a good 10-15 minutes walk from the center of town, whereas the small Coimbra station (not bigger Coimbra-B) is at the edge of the old town so very convenient. The regional train actually isn't that bad between Porto and Coimbra - I took a couple of trains in this region in May, and although they do make a lot of stops, the trains I was on weren't crowded and I had a few seats to myself. There are a few regional trains that go directly from Porto Campanha station to Coimbra without the change in Coimbra-B. (take a short train ride from Sao Bento to Campanha). There are faster trains between Porto Campanha and Coimbra-B, but then you still need to change to get to the smaller Coimbra station, as the fast trains stop only at Coimbra-B.