The first step is to ensure you are using proper Color Management practices by ensuring your Monitor is properly calibrated using a hardware device such as i1 Eye One Display2 or similar device.
You can find good advice at the link below.
Develop should be closer to any export than Library because Develop is working with the original file, not a cached preview as is the case with Library. There's also the export issue of fitting something into a smaller container. If you pour a 2L bottle of water into a 1L glass, you're gonna lose a litre of water. Exporting usually means taking a high bit expansive colour file and squeezing it into an 8bit sRGB file in a worst case scenario. You're simply going to lose information, and that's true in any application. You can control it a little with the choice of conversion engines, or with with rendering intent. Both of which are fixed in the case of Lightroom's export.
Personally, I only every see issues when I'm viewing files in non colour managed applications. Unfortunately, there's nothing any program can do about that.
Unfortunately, I don't think you understood my original post. The color quality isn't the issue, nor is the file size or type in exporting.
The issue is that what I see in Develop mode in terms of image clarity and sharpness is not what I see when I export (or when I view the image in Library mode). I understand that Library mode may be different, but I at least expect LR to export what I see in Develop. Like I said, I've seen TONS of posts about this issue and nobody has posted a viable solution yet on any of them.
I'll probably just switch to a different software because this is ridiculous. And Adobe does not have good customer service to help fix the problem.