In the game, the Chosokabe Clan have improved archers, the Mori have improved ships, etc. The only one that seems accurate is the Takeda Clan having improved cavalry, as Takeda Shingen's cavalry was renowned.
Besides Takeda Cavalry, however, is there any evidence that one Clan was regarded as having the best archers, ships, katana samurai, etc.?
Really hard to answer this as I have no idea what went on the game dev's mind when designing the game and don't know what sources they used if they used any. And it's really not possible to go into any kind of depth with this question, at least not without the game devs' input.
As the thread /u/GreatStoneSkull attached, Takeda is undeserving of its reputation of cavalry, at least on a Japan-wide scale. But yes, it does have that reputation.
If I had to guess, the Mōri are given ships because the Murakami clans (there's three separate large branches in the area) controlled much of the Seto Insland Sea, and they often (but not always) operated with the Mōri, and contributed greatly to the Mōri victories at Itsukushima and the first battle of Kizugawaguchi. Murakami's participation often gave the Mōri significant numerical advantage, though quality of ships is not really answerable IMO.
I have no idea where the Chosokabe bonus comes from. IIRC the first game it was the Uesugi who had the bonus so it's probably just because the game devs didn't know where to put it.
What are the other bonuses?
There’s a very detailed discussion of Sengoku cavalry here -
One of the things covered is the Takeda reputation for cavalry that appears to be based on a single incident that was told & retold. Suggesting that even the most famous ‘trait’ was little more than PR.