The 1927 Battle of Bennington / Vermont Independence Sesquicentennial Half Dollar is one of the classic-era US commemorative coin series that has a dual commemorative theme: 1) the Battle of Bennnington, and 2) Vermont Independence. (For a discussion of other "dual commemoratives," see:
Quick Bits #81 - Dual Purpose Commemorative Coins.)
The original coin proposal for the Vermont events, introduced by Senator Frank Lester Greene (R-VT) in January 1925, called for two coins to commemorate the pair of anniversaries: a gold $1.00 coin and a silver $0.50 piece. (You can read more about the two-coin bill and its objectives here:
What If? 1927 Gold $1 For Vermont-Battle Of Bennington 150th.)
Two events - two coins - it makes one think that the original intent of Senator Greene's bill might have been to secure two coins so that each one could be the focus for one of the anniversaries. A review of the bill, however, reveals that it does not include any language outlining such an objective. Such an omission wouldn't have precluded a two-coin / two-design / individual-focus scenario, however, as the design details were to be driven by the desires of the Vermont Sesqui-Centennial Commission, the coins' sponsor.
In any case, the Senate Committee on Banking and Currency removed the bill's provisions for a gold $1.00 coin during its review of Greene's bill and prior to a Hearing being held on the proposal. As such, during the Hearing on the coin bill, only the silver half dollar was discussed and recommended for passage.
It's certainly possible that, had the gold dollar coin been approved alongside the silver half dollar, the two coins would have followed the precedent of the 1922 Grant Centenary program and shared a common design. Who knows, a group of each may have also incorporated some device akin to the Grant's incuse star to create collectible varieties of the coins. Of course, it's also possible each of the coins would have incorporated its own distinct design but marked the same dual anniversaries.
With the Senate's removal of the gold $1.00 from the bill, we'll never know which of the three scenarios would have played out:
1. Two coins, two designs, separate commemoration on each;
2. Two coins, shared design, dual commemoration on each, or
3. Two coins, different designs, dual commemoration on each.
But nothing stops us from wondering!
My preference would have been #3 - a parallel to the 1926 American Independence Sesquicentennial gold and silver pair - two coins, two designs, same events commemorated on each.
1927 Battle of Bennington - Vermont Independence Sesquicentennial Half Dollar

For other of my posts about commemorative coins and medals, including more What Bennington-Vermont stories, see:
Commems Collection.