The Rambam wrote his Sefer HaMitzvos as a polemic against the Bahag's selection of the 613 mitzvos (as is clear from reading his Shorashim). They have many disagreements, which the Rambam lays out in his work.
From what I can tell, they both count a mitzvah to recite the Shema (Rambam Aseh #10, Bahag Aseh #1).
In the Machon Yerushalayim edition of the Bahag's work, they conveniently cross reference the Rambam's corresponding mitzvah number in the Bahag's list. When the Bahag has a mitzvah that the Rambam leaves out, they have the reference as a dash.
For some reason they have a dash after the Bahag's mitzvah of reciting the Shema. Unless I'm missing something, they don't disagree. Is there room to say they disagree? Or is Machon Yerushalayim mistaken (or is this a typo)? See below for a screenshot (the first one listed).
One potential avenue for an answer is the Rambam counts a seperate mitzvah of the Unity of Hashem, and I don't think the Bahag lists it. Maybe the Bahag includes it in reciting the Shema, although I don't see how that is evident.