At the highest level.... there is not much difference.
In the details, there can be differences.
Clearly, depending on what you select, the costs can vary widely but the transformers tend to be pricey.
The transformer *will* loose energy.... but one large inverter can be more efficient than two smaller inverters.
The transformer will create a true isolation between your AC circuits and the inverter. (This can be particularly handy if you are trying to isolate noise for something like a Ham radio)
A power transformer can be a big heavy item. This may not be an issue in a house, but in an RV or boat it can be a big deal.