RS3: Official client, and there's an Alt1 overlay I believe.
I only use the official client. I think there's a client through steam as well but unsure.
OSRS: Most people either use the official client or Runelite.
Money Making: You "make more" money in RS3 but the currency is devalued. PvM options in RS3 can range from 1-100m depending on your skillset.
OSRS caps out at about 5m/h through killing the nightmare.
You can see that 1m in RS3 will cost like 10fg, however 1m in OSRS will cost 40fg.
Pro's and cons:
RS3 Pro's:
Stronger story line, more developed quest lines
Better PvM/PvE
Interface customization
Larger endgame
Less "grinding" meaning you can level faster and progress easier. Spending less time.
"Better" graphics (I mean more updated)
Combat mechanics are better. You have more control over your character and can "combo" abilities together.
More overall content.
RS3 Cons:
PvP is pretty much dead. Like maybe 100 people do it outside of one specific event per day.
Micro transactions. Some people view it as giving an unfair advantage.
Lots of dead content once you pass a certain level
Compared to some other MMO's, combat isn't the greatest. Still reliant on the tick/tile system.
Cosmetics/overrides can sometimes be overwhelming and ruin the immersion into the game.
OSRS Pro's:
Better PvP
No micro transactions
Longer grind, can provide sense of accomplishment
Nostalgia to those who played before things changed
Updates are reliant on a community vote so you have a say
Mid game and early game content stays relevant
OSRS Cons:
PvM is stale except for a few exceptions. PvM is centered around clicking the enemy and waiting for it to die.
Dated graphics
Lacking end-game due to the grind it takes to get there
Personally, the community seems relatively toxic, but that's a personal anecdote.