I own a BVK but haven't looked at a Loop Q so only going off the specs for it.
First off what type of rod are you looking for? What weight? Targeting what species? Streams, rivers, lakes? Dry flies, nymphs, indicators, streamers? Its not really possible to give you a good idea on what rod to choose without knowing how you plan on using it.
Assuming you want an all around trout rod say either a 5 or 6 wt the main difference you will notice is that the BVK is a faster rod. The BVK is a fast rod(even by fast standards) whereas the Loop Q in those weights is said to be a medium fast. The Loop Q is also a heavier rod, over 4 oz for the 5 wt and 4.5 oz for the 6 wt compared to 3-3.2 oz for the BVK. I am surprised by how heavy the Q is but swing weight is more important then overall weight and the BVK has a high swing weight.
The BVK will likely toss larger flies, streamers and indicators easier. It should cast farther and into the wind easier. The Loop should offer more finesse, work better for dry flies, and give better accuracy on shorter casts. Which one is best will ultimately come down to personal preference and fishing style.
And just googling it I found the following which has some good information confirming most of my thoughts(albeit in the 8 wt size).
https://www.yellowstoneangler.com/ge...rod-comparison
Note that the Loop Q in 8 wt is called fast action but it is still slow compared to the competition, in the 5/6 wt classes the BVK is likely a significantly faster rod.
I am thinking the weights on Loops website might be wrong. They say an 8 wt should be 190 grams(6.7 oz) whereas yellowstone angler weight it at 4.1 oz. The swing weight is lower then the BVK which will offset its higher weight. Swing weight is one of the biggest differences I notice between my BVK and NRX, even though they weigh roughly the same the NRX is easier to cast all day.
I personally would probably go with the BVK but I like fast rods for the fishing I do(mostly casting indicators or trolling sinking lines).