Why use a gaussian low pass filter, when we can convolve with gaussian kernel
In practice gaussian low-pass filters are written using F.I.R. or I.I.R. filters, first the filter runs left then right on each horizontal line, then the filter runs up then down on each vertical line.  It's much cheaper than doing FFTs and IFFTs.

Your two operations are not performing the same operation.  The effects of the filtering around the edges will be very different.  You are doing a circular convolution.  For the Discrete Fourier Transform the convolution theorem says that the multiplication of fourier transforms is equivalent to convolving the image infinitely repeated/tiled in the plane.  So around the left edge, for example you are blurring together some components from the right side of the picture.  (For example try performing your operations on a picture that is black on the left half and white on the right half.)

Your "low pass" filter is padding the image and the kernel to try to reduce some of the edge effects.  It's more expensive, but it is closer to what you would get if you did a "real" convolution of a gaussian with your image.

In your application the circular convolution effect of blurring in data from the other side of the image may be okay, but in many application it is unacceptable.

As to the reason that the FFT of an $N\times N$ image is 10 times faster than the FFT of a $2N \times 2N$ image.  A 2d FFT is done by taking 1d FFTs of each horizontal line, then 1d FFTs of each vertical line.  So in the $N \times N$ case you are doing $2N$ 1-d FFTs, each of which take $O(N \log N)$ for a total of $O(2N^2 \log N)$.  In the $2 N \times 2 N$ case you are doing $4N$ 1-d FFTs each of which take $O(2N \log 2N)$ for a total of (a little more than) $O(8N^2 \log N)$.  Add in cache effects for the larger image and 10x slower seems quite reasonable.