Fill a crack in the granite countertop

The big difference as you mentioned is price. The seams with the pre-cut pieces should not be an issue (assuming the installers are good at what they do), the more noticeable factor will be the difference in colors and patterns.

If the entire counter is cut from a large slab, the colors and patterns will be consistent throughout the entire counter. If the counter is assembled with pre-cut pieces, you may notice differences in colors and patterns from one piece to another. The choice here, however, would come down to preference. Some people might prefer the look of one method over the other, so it's hard to say what you'll like better.

I would find out if they have a show room or can provide pictures (from previous jobs) of the different methods, then you can decide which you personally prefer (while keeping your budget in mind).

There are a lot of bad fabricators installing granite these days. I have seen everything from edges that are waxed instead of polished and tops that are dyed to make them look like a more expensive stone than the fabricator purchased. If they did a bad job there is no reason to believe any of it is done right.

Do the water test suggested above. It will tell you if it needs sealing. It likely does. I would also watch the edges. If they start to go dull in a few months then you really got taken. Polished edges will last a lifetime. Waxed edges a few months. Polishing takes about 15 minutes a foot with very expensive tools. Waxing takes seconds with cheap wax. This is only one example of many tricks to pass off bad granite countertops.

All granite countertops are not created equal. If you purchased from a guy with lawn sign working with only a cell phone as many today do you got what looks like a good price for a countertop but wait until you try and get warranty work. Good luck because if your installer did not know if it was sealed and you are already doing corrective work you are likely to be even more disappointed in the future as the top ages.