Not really much difference, at least at face value but in daily use LLDPE are probably more resilient and have the additional benefit of thinner wall thickness. This has great advantage, in shipping and storage, and when gathering the neck to tie a bag. They accept adhesive labels and indelible marker better that traditional polyethylene, making labelling and tracking easier though there are better ways to deal with this. Overall, they are substantially lighter.
On the downside, the tear resistance is perhaps somewhat less, and they are ever so slightly translucent, but not transparent, leading some to reject them on the grounds of aesthetics. Cost differences are largely negligible. The makers of the heavier polyethylene bags claim better leak and tear resistance but puncture resistance may be less favorable and overall the differences are perhaps marginal if not non-existent.