Shadow has a similar level of anonymity as cryptonote coins without the bloat and scaling problems that they have.
That's second part is nonsense. It uses the same methods and has the same bloat and scaling problems (assuming they are actually problems that aren't solved by ongoing improvements to technology), albeit with reduction in signature size by a bit less than a factor of two.
Is it? Shadow blockchain is about 400mb. How does that compare to Monero and Aeon?
The difference is all about usage. There is no scaling/bloat advantage to Shadowcash other than the LLW signatures that are less than a fixed factor of two smaller on large mix factors.
EDIT: Oh and I forgot, Shadow uses 1235 denominations instead of 123456789 so there are more signatures needed for most payments. That should somewhat offset the LLW and leave the two almost identical in size.