I assume you mean you're using the same monitor on both PCs, and the image quality is worse with the new PC than with the old PC?
VGA is an analog standard, and can be affected by all sorts of noise and signal degradation. It's not at all uncommon for different video cards (or in your case, a HDMI to VGA adapter) to result in blurry images, dim images, wavy images. It all depends on the quality of the digital-to-analog converter used by the video card (or the HDMI to VGA adapter), and the shielding around the circuitry.
You can try a different HDMI to VGA adapter - that will produce a different image, maybe better. But since your monitor is only 1366x768, I'd suggest you stop wasting your money on HDMI to VGA adapters. Retire the old monitor and buy a new 1080p monitor that accepts digital input (HDMI, DVI-D, Displayport). The digital standards are exact and error-corrected. So the image the video card sends is exactly what the monitor receives - no image degradation along the cable.