Although you my be able to connect to the internet with either device, the two are quite different from each other. Something to keep in mind in regards to IP addressing. There are public IP addresses (the IP of your modem), and private addresses (the IP of your computer(s) and/or router). You see, when you connect a modem, it is issues a public (WAN) IP, static or dynamic, from the internet provider. If you have a router, it will have its own private (LAN) IP - typically the router will distribute additional LAN IP addresses to any computers connected to it, unless they have statically assigned LAN IP addresses.
In other words, when someone "hacks" you, if they get your IP it will most likely be your public, WAN IP that is assigned to the modem.
There are a number of benefits to using a router, but rarely are there security benefits. If you want to be safer, you need to take additional steps, such as installing a firewall, virus and malware protection, and keeping your system/software up to date. These are the most important things, if you have these setup (properly), it doesn't matter if you have a router or not. Now of course there is always an exception to this rule, as some routers offer a built-in firewall, and other security features. However, most consumer grade routers will not provide better protection than you can find by using software installed on your computer(s).
I hope this answers your question. If you are still concerned about anything I've said here, please fel free to let me know and I'll do my est to answer accordingly.