My understanding of Freelancer is that it's closer to Wing Commander Privateer; you have your own ship, and undertake missions as a freelancer, hence the title. The Freespace games have you as a pilot for a military instead of for yourself.

I've played both games and they are not really comparable. Freelancer as you, I guess, know incorporates a trading system and relative freedom of choice where you go and what you do. Freespace on the other hand follows a mission driven story with a military background, as boct1584 already pointed out. It is more akin to Games like Starlancer or the Wing Commanders, Privateer excluded. If you're searching for a free form style of gameplay where you can trade and make your own choices Freespace might not be for you, instead I would ,for all its quirks, recommend the X series. If you're looking for a story driven game, on a mission to mission basis, which gives you sometimes indirect Control over small units of spacecrafts as squadleader (per orders like Protect, Attack etc.) you will be well served with the Freespaces. There also is the Freespace 2 Source Code Project which offers enhanced graphic and a lot more, it should be linked in these Forums, as well as a load of other Mods as well. Beware though, compared to freelancer, that you always have direct control over your ship so no clicking on icons to fire your weapons or to set the course, you'll have to fly yourself and shoot yourself, so a Joystick is recommended but according to some not necessary.

Okami123 has it right, they're different games really. Both are utterly awesome though, I highly recommend them.