Welcome to the forums.
When you have two options, one is better then the other. One method cannot be bester over the other after all. I point this out because it is a forum rule, no option is best. There may be an option better suited for a certain situation to a certain individual, but best is arbitrary and not worthy of arguing over.
As a general rule: if the welds don't affect fitment with a panel, it would be advisable not to grind them down. Some of those welds look quite boogery, which usually implies low penetration. That in turn means if you grind it down the panel can just come undone at the seam as it was a poor job of fusing the material.
The quality of the job depends on how well the welds penetrated. A whole continuous bead will be useless if penetration was low and the panel falls off. Similar with the stitching method if the tacs are weak the panel can easily perforate and separate. The problem is it is difficult to judge a weld hidden under paint even more so under seam sealer. The visible beads don't give me much confidence though.
Personally I used to like welding a bead all the way around, but it is very time consuming and has a very good chance of warping, that's how I did my car the first time, but when I had to cut it out it out to shift my floor it took forever to grind down all the welds.
My current preference would actually be somewhere in the middle, about 1/2 an inch to an inch long seams with gaps, the gaps can be filled in with seam sealer to keep the joint water proof. Takes about half the time compared to filling in the whole panel, also introduces less heat if you move around, and as long as the penetration is good will hold just find. Second time I did it I stitched and seam sealed.
So to answer your question, it depends on how well the panels are fused. The thing to consider is that cars do flex a bit. If you put all that heat and make that one part stiff, there is a chance that as that part cools or as it is in service it can pull at pieces that aren't as stiffly connected.
If you can't weld then not much you can do about it unless you have the funds to take it to a proper body shop and have them have at it, but most body shops are more panel replacement places, not too many restoration places in service. As long as the second place you went to didn't use seam sealer to hide their work I would say the second place did a more favorable repair. I would say you should still seam seal the welds from the first place as it looks like it is fairly raised which means most likely pin holes are present which can cause rust to start forming if paint did not cover it well.