I've used Montway several times in the past. Highly recommend. Originally used them based on Rennlist recommendations, and I haven't had a bad experience with them. If shipping something high value, I would use someone all internal like Reliable, but I wouldn't bother with these cars.
With the exception of the internal carriers, these companies are all brokers that post your request on a national board and try to match you with a driver. How they differ can be important though. A few things I've learned fwiw:
1. Price. If your order is posted below market value by your broker, there may not be a company/driver willing to accept if they can just pick up something else at fair value. Some of these brokers will lowball quote you to get you to post with them, and they'll post you below market. If you can't get a transport, they will suggest you can pay more to increase your offer. This may get you the lowest price possible, but it may also delay getting your car.
2. Customer service. Smaller brokers can usually quote you slightly lower prices, but their customer service can vary wildly and may depend on how Junior happens to feel that day. Large brokers like Montway have a reputation to protect and necessarily have to provide good communication to stay in business as a result.
3. Insurance. How rigorously your broker verifies the qualifications and insurance of the drivers they match with can be a big deal if something happens during the trip. Any reputable broker will supply you with a copy of the insurance policy of the transport company when asked. If they won't, DO NOT USE THEM. This is a huge red flag. Also those policies may not cover some things like hail, road debris, etc. I would advise reading it and deciding if you need additional insurance before it ships.
4. Phone calls. If you request a quote through one of these sites that gives you multiple quotes, be prepared for a barrage of phone calls, emails, text messages, etc. everyday from multiple brokers. I did this once just to see how Montway compared. For me, these only lasted until the car was shipped, but I know others who have gotten them weeks after their car was shipped.