These are very different approaches. The first tries to account for technical variation between the two sets, mapping similar cells between the two to each other. The second literally just merges the columns and rows of the two sets together into one object - it's not doing any special normalization. It's just a straight merging of data.
It's tough for us to say which is more appropriate - the first may help you to identify cell populations that truly differentiate the two, but it could be blowing away real differences due to how Seurat's integration works. It will force populations that aren't similar together if there aren't many overlapping cell types between the two samples. The second may be revealing significant technical variation or batch effects, or it could just be that your cell lines are quite different from each other. You are in the best position to determine if this is the case or not - we know nothing about your samples.
This is where the true difficulty of RNA-seq analysis lies - nobody is really going to be able to tell which is truly correct.
You might try other integration methods if you feel you have batch effects or technical variation that needs to be addressed. I've found the SeuratWrapper around fastMNN to be quite good, personally, as it handles cases where samples don't have much overlap in terms of cell types much more appropriately.