I've had had problems with both of these (and tried all or most of the main ones) From time to time the shared IPs get blacklisted and you get fails with some people's email providers. They fix it eventually, but to avoid it you'd need to pay for a dedicated IP. e.g. with mailgun I contacted support to say it was happening after checking my stats. It took a day for them to respond but then they did switch IP.
You can see in my last month stats.
You can also get some issues with Amazon SES - I find mostly with btinternet - but at lease with Amazon you get email notifications of fails so you know immediately.