This has really been bugging me. There are many things that make me think
that it is. For starters, there is no Myria in this game. She was the
Goddess in Breath of Fire 3 that tried to control the world. At the end of
the game she was killed, which would explain why she was not in this game.
Also, in Breath of Fire 3, the World was two halves, east and west, that were
separated by a giant ocean and Myria said that if she did not keep the desert
back with the ocean, then it would cover the earth. Well, in Breath of Fire
4, the world is covered in Mud, and much of the world is desert. How do we
make Mud? Water and Sand, and what could make more mud than a desert that
ran into an ocean. And if you notice, Wyndia is on the eastern continent
like it always is.
Another hint that the two stories are connected is through the appearance
of some of the non saga-orientated characters(i.e. Mogu, Gary, Bunyan) such
as Rei(renamed Rey, but it's the same person/tiger) and Teepo. These two
open up a shop and sell things in the clear game of BoF4. Could this just be
an easter egg from Capcom? It probably is, but the fact that the two are
there suggests some sort of connection.
There is also the occurrence of Momo as a master in BoF4. She herself says
that she was working in her laboratory when there was an explosion and she
was knocked out, and the next thing she remembered was being in a different
place, like a parallel dimension or something.
Then there is how the dragons are brought from one world to the world of
Breath of Fire 4. It is explained that the dragons were brought to be gods
in this world from another one. Deis and Ryu were not brought correctly and
thus, Ryu was split in two and Deis wound up in a talking and walking garbage
can. Maybe there exists some type of Dimensional Rift in BoF3's Dragnier
that connects it to BoF4's Chek, the two certainly look enough alike for that
to be possible.
Another similarity in the two is how many of the skills from 3 are in 4,
even some of the same enemies. This is not very major, but I still think it
is worth mentioning.
This isn't really all that major, but the design on the Breath of Fire 3 cd
is similar to the disign of the Breath of Fire 4 cd, only in 3 Ryu is on the
cover and in 4, Fou-Lu is on the cover.
This is only what I can remember, there may be more connections that I've
not found yet or can't remember at this time.