Sunset Riders plays like your average Contra style run n' gun game with the high jump from Rolling Thunder/Shinobi added on, it has you moving through a wild west setting shooting the enemies and collecting weapons power-ups which either give you a second gun or the ability to rapid fire. One of the more notable aspects of the original was the fact that it had a 4-player co-op which was quite rare for the time (the 4-player mode is missing from both ports).
SNES - The gameplay here is relatively accurate to the arcade game, but its sadly missing the 4-player co-op, and the it's more difficult due to the fact that you get put back to the start of the level when you use a continue (which I actually take quite an exception to as dying on a boss only to be put back to the start is frustrating as hell and doing each level with 3 lives can be tough), thankfully however this does not happen in 2-player mode.
The biggest exception to accuracy within the levels is the aforementioned Level 5, which has replaced the Indians with generic cowboys (the Indians actually had different moves so this changes the gameplay of that stage somewhat).
Mega Drive - This version has loads of very big changes. Only half of the arcade levels were converted here, but the levels that were converted have been lengthened and split into two stages each (basically the level progression goes Level 1 -> Level 4 -> Level 5 -> New Level). The last level has been completely replaced by an original stage in which you're storming a mansion in the rain whilst being attacked by dogs, this level whilst pretty good, doesn't really do anything new. The changes to the level progression have the affect of making the game pretty much the same length as the SNES version but much more lacking in variation by comparison.
The bonus stage where you have to shoot as many enemies as possible has been replaced by a horseback riding stage where you have to catch items being thrown by a carriage, the new bonus stage is fairly fun to play, I'd say that though very different it's still pretty much as fun as the original.
The last drastic change has been made with the boss of the train stage as El Greco has been replaced with Paco Loco (The boss from arcade/SNES level 6) Paco's moves don't fit in well with the new environment.
Where it comes to the main gameplay. Bullets travel faster here making them much harder to dodge, and unfortunately making this version cheaper, and less fair (it's more based around trial and error), and shooting the Dynamite now detonate's it which has mixed consequences (yes it's cool to time the detonation to blow up the enemies but it's much less helpful when you're already firing and dynamite's thrown into your line of fire next to you)
On the upside the Indian level (SNES level 5) is actually much more accurate to the arcade than the SNES version as it retains the indians who fire flame arrows (the SNES version replaces them with cowboys), it's bridge section drops as you walk across it, and the lift section has also been retained (this was replaced in the SNES version by a hand over hand rope section). You also now have a stand-still-and-aim ability which is very helpful in certain situations, and is definitely a good addition (as it means you can fire diagonally without walking in that direction)