1 - No equity. The legal company structure prevents you getting equity in the company.
2 - Significantly reduced employment rights. During the current waves of layoffs people employed through these type of arrangements found they had significantly less rights than normal employees, primarily due to fewer people being employed this way did not meet the usual thresholds for redundancy planning and payouts.
A friend of mine employed through an employer of record was "made redundant" and was offered exactly zero notice, severance or payout. When he tried to negotiate they effectively told him to sue them, knowing it will take significant time and legal costs to bring forward a claim.
Legal differences can be significant - for example, in France it may be difficult legally to ask an employee to put in more than their contracted hours compared to another country where this could be very normal.
A recent example in the news is the Twitter layoffs - in the EU they may have enacted layoffs that aren't legal there but are perfectly legal in the US.
Taxes in different countries can mean there's a significant difference in the difference between the amount an employer pays and the employee receives per country. Sometimes it's negligible enough for the employer to foot the bill, sometimes it's large enough they may need to pass on the difference. This can get even more complicated when share options come in to play.
If you are responsible for this it all really starts to add up, ultimately the more countries you employ in, the more cognitive overhead which can impact an organisation's agility (or require them to take more risks).
The difference is that Twitter is likely to be bankrupt by the time any American lawsuits get resolved.