So I'm staying in a Best Western Hotel for around 7 nights and would like to use my rewards for either United Airlines, American Airlines, or Delta (or maybe for additional Best Western Hotel stays, if that is more efficient). Is the rewards program for Best Western more efficient for some airlines than others? And price-wise, does it pay more for additional stays at Best Western, as compared to additional frequent flyer miles?
There's no single answer to questions like this, as they depend on what your future travel plans are going to be.
For example, 1 United Airlines mile is worth less than 1 cent if you use it to buy a Gift card, 1-3 cents if you use it for many economy domestic flights, or as much as 10 cents or more for some itineraries such as international first class. That's a factor of over 10 times, depending on what you use the points for!
Specific to Best Western points, unfortunately they are not the best in the industry. You'll earn 10 points per dollar, but redeeming for a free night will cost anywhere between 8,000 and 36,000 points - so that means you'll need to spend $800 to $3,600 to get a single free night.
If you instead decide to credit to your airline frequent flyer program, most of their earn rates are per STAY, not per night or per dollar. This can work out well for a single-night stay, but not for a 7 night stay like you've got as you only get the same number of miles as you would for a single night! Best Western do allow you to move points to an airline after the fact which will give better rates for a longer stay, but they are done in "lots" of 5000 points (which turns into 1000 airline mines), so if you've got 9,999 points you can only transfer 5000 of them. 5000 points = 1000 miles, which based on the math above is worth somewhere between $10 and $100 - depending on how you end up spending them!