(Note: This will not include the VC and mobile versions (though said mobile versions are possibly Dotemu ports and were possibly ported for Steam), since I've never played those ones. I doubt it that they play the same either way comparatively as the MVS/AES versions, but they might or might not have issues.) Ditto with the Switch versions, never played them.
Ports and Differences:
MS1:
1. MVS/AES: The originals, no problems there.
2. PS1/Saturn/NG-CD: Load times and cut animations vary, plus mission select, but includes combat school and art gallery depending on release.
3. PS3: NG-Station port done by M2 that's seemingly comparable to the MVS/AES originals with various options, along with online co-op.
4. Steam: Comparable to the PS3 port, but may have music/sound issues and maybe some other issues. Game runs a bit faster than normal. Also has online co-op and mission select.
MSX:
1. MVS/AES: Originals
2. PS1: Has load times between and cut animations plus mission select, but includes the combat school, art gallery, and another mission. (Blood types vary within region versions...JP PS1 has Red, US/EU has White.)
3. Steam: Comparable to MVS/AES, may have issues the same way as MS1, but really minor. Plays in normal speed. Also has online co-op and mission select.
MS3:
1. MVS/AES: Originals
2. PS2 (PAL/JP)/Original Xbox (All Regions): Plays the same as MVS/AES (dunno if these releases have a mission select.), includes bonus mini-games Storm the Mothership and Fat Island (only these console versions have these mini-games). (Note: The US OG Xbox release is strict for continuing, as it will send you back to the beginning of the mission if you use a continue. JP and EU regions doesn't do that and it respawns you back to where you died)
3. Xbox 360: Straight 1:1 port. Though its just a barebones port with no extras. (Blood is set to White if the 360's system is set to any language that isn't JP, which though makes the blood Red. It has online co-op, but its connections are unbearable for this port.)
4. PS3/4/Vita: Straight 1:1 port. barebones. Though this port has innaccurate difficulty settings, but it does have online co-op, and connections vary.
5. Steam: Also comparable to MVS/AES, may also have issues, but also really minor, also plays normal speed, and also has online co-op and mission select, gallery only for this one.
MS4:
1. MVS/AES: Straight port. Includes a gallery mode which doesn't actually work for some reason.
2. PS2/Xbox (standalone): Has functional gallery. Has a weird bug where sound effects stack, making it a VERY LOUD game. Was later bundled with MS5, although as far as I know it's identical to the standalone version.
3. Wii: Port of the AES version. Has white blood. Additionally, European players get white blood and it's in 50hz, so seriously do not buy this it is a bad idea.
MS5:
1. MVS/AES: S T R A I G H T P O R T.
2. PS2/Xbox: Released packed with MS4. The game tracks your best times for individual levels and full runs, and has the now-obligatory prisoner record and item collection sections. PS2 version has some weird stuttering issues (I don't know if MS4 has this too). Most importantly, there's a weird bug where the ending goes so fast that you can't hear the full credits song (Boooo . . . ).
MS6:
1. PS2 version has combat school, art gallery, etc.
MS7/XX:
1. Originally came out for Nintendo DS. All of the ports are the enhanced "XX" version, which I haven't actually played but as far as I know have alternate routes, more enemy variety, etc. No differences between them besides that.
Side note: There was a separate anthology game released in Korea and Europe called Metal Slug Complete PC (also known as Metal Slug Collection PC), with the same lineup as Anthology (so no MS7/XX). Beyond a poorly-implemented music test there's no extras like Anthology, no video options at all, save/load state options that only work in a single game session (if you close and try to load, it crashes) and control settings that don't recognise joypads (get Joy2Key on standby for this one) and make setting controls for two players impossible without Joy2Key, it seems. On the plus side, it has slightly better emulation than Anthology. Not an ideal way to play the game, honestly.