Printing on paper from digital scan version versus from negative

"Quality" is a loose term. Was your film a 6x7 that you wanted to turn into a 40"x60" gallery print that was simply scanned for backup? 'Cause if so, I got bad news for you.

Or, was this a 135 shot destined for a 4"x6" to hang on the fridge that got scanned at a ridiculously high resolution for...reasons...?

Maybe it was a 135 shot scanned at a normal resolution that would allow you to take the image up to the normal 8"x10"?

Whether scanning & printing or darkroom printing, there is a maximum size that you can take the image before things start to fall apart. As long as you are staying under that theoretical maximum, then "quality" differences between the two methods are effectively null (that is, unless you've run into a forum full of purists).

The kicker here is the scan quality. Scanning introduces variables that can detract from the image, reducing the "quality." But, if it is a good scan at a decent resolution, then you should have no problem getting a print made. In fact, you can still get a print processed in chemistry, known as a C-Print. Though, don't discount inkjet printers, they've come a long, long way.

If you are absolutely, dead set on printing in a darkroom, then you can digitally invert your image and print it on transparency paper and then contact print it in the darkroom. Note: this absolutely will reduce detail/clarity/sharpness. I do this to go from digital to experimental processes (platinum/cyano/etc) and have not ever gone from neg to digital to transparency to paper. That many jumps would be sure to degrade detail, but it may still be a fun process to go through for you.

Now, if it is a junk scan, then you have a lot of work to do to even attempt to get a small print from it, and if that is the case, then I suggest you ask a new question on how to adjust the image to prep it for print at a certain size...add the image to the question as well.

Short answer: if your film lab is careless enough to have destroyed your negative(s) after scanning, their scans might well be junk, too. However, if you have the file, you'll be able to judge for yourself. In general, to make an 8x10 optical print that doesn't look pixelated, you'll need a couple megapixels -- which is usually less than common lab scans, even the "basic scan". So you ought to be okay there.

The down side is, the scan you have is most likely lossy compressed -- a .jpg file. This file format makes a much smaller file from a given image by literally discarding part of the information from the scan. Depending how aggressively this was done, you might have a file that will make an 8x10 print almost indistinguishable from an optical print made from the negative, or you may have a scan that won't look good as anything bigger than the thumbnail image on the screen.

If you have .tiff, or high quality .jpg or .png files, you should be good to go. You can upload your files to any local print-from-digital service (Target and Walmart have these, many drug stores do as well) and get prints back, often within an hour or two. Some will be ink jet and some dye prints of one sort or another -- and they'll be nearly indistinguishable.

Either way, I'd probably avoid using the same lab again. You might even consider getting the equipment to process your own negatives. Even color (C-41) is pretty easy these days, and even the least cost-effective method (small capacity chemical kits -- 1 liter of each solution, processes about 8 rolls) will cost less than lab processing. You'll need to buy some equipment (developing tank, changing bag, some measuring and mixing vessels that will never be used for food or drinks) and if you don't already have a high res digital camera, you'll need a scanner to get digital files from your negatives -- but a $200 used scanner can do what's needed for 35mm and 120.

Once you're doing your own processing and scanning, you don't need to worry about the lab losing or destroying your negatives, or about them getting damaged in the mail (if you're sending them off remotely).

Is it possible to achieve the same degree of quality in printing on paper from the digitalized version, as if it were from the negatives?

The quality of prints you can obtain with the digital file you possess depends on the properties of the file and image, including resolution, sharpness, and color fidelity.

Modern labs use digital intermediates to create prints. Prints made directly from the digital intermediate would be indistinguishable from prints made from negatives.