I'm from Inner Mongolia. What people are saying in the comments are basically true. China has been making Inner Mongolia more Chinese for a while. Most people in Inner Mongolia don't speak Mongolian, like they have zero knowledge even though there are Mongolian words on every sign on the street. You can probably experience some Mongolian Culture there, but it's pretty mild compare to Mongolia the country. You still can get authentic cultural stuff on the grassland but not anywhere near the major cities. Normally it takes 3 hours ish to go to places that still keeps the original culture from major cities.
Crime rate wise, you don't need to worry too much, Inner Mongolian people are pretty rich. You can see a lot of BMW, Mercedes, Porsche and even Lamborghini in cities like Hohhot, Baotou, and especially Erdos. There are crimes granted, but since China doesn't allow citizens to own or carry firearms, nothing big can happen. If you are a somehow muscular guy, most crime will stay away from you. After all, they have to be able to communicate with you to rob you. If you don't speak Chinese or just pretend not able to, no one would bother taking the time to rob you, there are bigger and easier fish in the pond. Just be sure don't get fake married on the grassland, they charge a lot....
I cannot speak for Mongolia because I haven't been there. But rumors suggested that your worries are somewhat not unnecessary.
To reply some of the comments. You surely can find some of the cultural stuff in the cities. However, tourist scam in China is a real thing, they normally would get you into a temple, say your life is unfortunate, but if you spend 500 dollars on this candle and light it up, your life will be turned around. If you don't pay they would just keep saying bad things. It was really really sick. But I have been out of there for 7-8 years, I can't really say that's still the truth. But one thing for sure, if you are looking for authentic cultural experience, you have to find a local person to take you to the grassland, where tourism isn't their main source of income.