Disclamer: I don't know almost nothing on CNNs and I have no idea where I could ask this.
My research is focused on high performance on computer vision applications. We generate codes representing an image in less than 20 ms on images with the largest size of 500pxs.
This is done by combining SURF descriptors and VLAD codes, obtaining a vector representing an image that will be used in our object recognition application.
Can CNNs be faster? According to this benchmark (which is based on much smaller images) the times needed is longer, almost double considering that the size of the image is half of ours.
I would be wary of benchmarks and blanket statements. It's important to know every detail that went into generating the quoted values. For example, would running CNN on GPU hardware improve the quoted values?
20ms seems very fast to me; so does 40ms. I have no idea what your requirement is.
What other benefits could CNN offer? Maybe it's more than just raw speed.
I don't believe that neural networks are the perfect technique for every problem. Regression, SVM, and other classification techniques are still viable.
There's a bias at work here. Your question reads as if you are looking only to confirm that your current research is best. You have a sunk cost that you're loath to throw away, but you're worried that there might be something better out there. If that's true, I don't think this is a good question for SO.
"I don't know almost nothing on CNNs" - if you're a true researcher, seeking the truth, I think you have an obligation to learn and answer for yourself. TensorFlow and Keras make this easy to do.