Single big BST vs multiple smaller BSTs? Which is faster for search? Lets say that I am storing 10^9 keys in a single BST. 
Compared to having lets say having multiple BSTs of sizes 10^6 containing chunk of the bigger tree? Search through all of them executing in parallel.

I am talking about only search performance here, Given that processing power is not a bottle neck.
Searching among $N$ in a BST takes (roughly) $\log_2 N$ comparisons. So searching in $10^9 \approx 2^{30}$ takes around 30 comparisons. Searching in $10^6 \approx 2^{20}$ takes 20 comparisons. The cost of farming out the work to 1000 processors, collecting the results and figuring out the answer is surely costlier than 10 comparisons.