Loads of people have actually played Privateer here, myself included.
Based upon the original - I never played the sequel or remake, the main differences IMO are;
1/ Privateer uses a different physics system; you can, for example, slide. FS2s is considered somewhat more realistic IIRC, although it's still a simplified non-newtonian (arcade) model.
2/ Privateer focused on the player being alone, fighting battles against a small number of enemies or in some cases a single large vessel. FS2 normally has the player fighting with allies (wingmen, allied capital ships) in a more military situation against multiple large enemy ships.
3/ Privateer allows the player to communicate with enemy ships to insulte / placate them. FS2 communication is used to allow the player to order their allies.
4/ FS has support ships which rearm/repair their vessel on demand (these may be unavailable on missions which demand it for realism); Privateer doesn't
5/ FS2 has beam weapons and flak; neither IIRc exist in Privateer
6/ A key part of Privateer was buying and upgrading your ship (armour, engines, etc); FS only allows the player to select their ship & weapons
7/ The player is a fairly anonymous fighter pilot in FS2, within a military organisation. In Privateer the player is a cargo trader / merc / pirate; as a result both have different 'feels'.
8/ In FS2 the player flies fighters and bombers; the ships in Privateer are generally larger and several are cargo vessels.
9/ In Privateer (if they are added to the ship) the player can control their ships turrets by switching position
10/ The player cannot autopilot between systems in FS2 (note; this is being / added for the WC TC, though it's not used in the main campaign or AFAIK any existing mods)
11/ AFAIK FS2 has many more mods than Privateer
Um... there's probably more, but you get the idea.
I actually liked Privateer a lot, so I'd recommend it. The only caveat is that I found the combat pretty unsatisfying; most my attraction was actually souping up the various Galaxy / Centurion ships I owned.
EDIT; I've not played any recent remakes of it, though.
