Quantum vs. regular computing time to break ECC?
It's hard to answer given that there is no quantum computer to perform benchmark on. However, let us assume a quantum computer which would perform quantum operations as efficiently as our current standard computer can perform classical operations (this might be a bit unrealistic but it's hard to come out with realistic assumptions regarding quantum computing given the state of advancement of this research field). The complexity of Shor's algorithm being $O(\log^2 n \log \log n \log \log \log n)$ according to Wikipedia, one can observe that this is better than the complexity of the best known classical algorithms for performing the multiplication of two $\log n \times \log n$ matrices. A quick search over some papers such as this one indicates that an optimized implementation of matrix multiplication of size $1024\times 1024$ can take less than a second, hence it does not seem unreasonable to assume that if a quantum computer was executing an optimized implementation of Shor's algorithm, factorization of a 2048 bit integer would take very little time - say, less than a few minuts.

For a regular computer performing a discrete logarithm over an elliptic curve is not done with brute force as you suggest, but using the Rho-Pollard algorithm, whose complexity is $O(\sqrt{p})$, where $p$ is the order of the curve. Still, executing this algorithm on well-chosen curves of size higher than $256$ bits is completely impractical.