Aoi Tokugawa Sandai (2000)

Both dramas portray Ieyasu as the protagonist, but Aoi is only focusing on the older Ieyasu (to be exact after Hideyoshi death). Both dramas however have different interpretations on the character, where TI is more on the whitewash version, while Aoi is skewed towards the "gray-character" which in my opinion more tally with the historical records.

If you want to know more about Japan politics especially the conflicts after the death of Taiko, Aoi has the best depiction and it is also one of the best and comprehensive drama discussing Battle of Sekigahara, which is the final moment in Clavell's Shogun.
The difference is Aoi follows 90% of the actual history while Shogun as we know does not.

Bonus: Miura Anjin (Blackthorne) does have an appearance in Aoi

Downside:
1. Aoi is 49 episodes long and span over the 3 generations of Tokugawa
2. Aoi has low budget compared to Shogun for obvious reason
3. Aoi has old actors playing younger role

Aoi is another portrayal of Gou-Hidetada marriage life. However Aoi started off with both of them already married (i.e. it will not start from their childhood) and focused more on the affairs around Tokugawa big family as well as more details on Edo shogunate administrations.