Is there a better way to check if a value is not equal to another value?

You are connecting a PlayerAdded event to your function every second. If a player joins after 60 seconds, this means that your function will run 60 times!

Fortunately, we don't need the loop at all -- just listen for the Changed event.

local DataStore = game:GetService("DataStoreService"):GetDataStore("Cash")
game.Players.PlayerAdded:connect(function(player)
	local key = "user_" ..player.userid
	local v = player:WaitForChild("Value") --I will assume that this 'value' is the Cash Int/NumberValue and that v.Value is the actual amount of cash
	v.Value = DataStore:GetAsync(key) or 0
	v.Changed:connect(function()
		DataStore:UpdateAsync(key, function(oldValue)
			if oldValue == v.Value then return end --returning nil cancels the update
			return v.Value
		end)
	end)
end)

However, according to the API, datastores may error unexpectedly, which is why I recommend wrapping calls to the datastores in pcall. I've written a small function, "Try10", which will attempt to run a function up to 10 times before giving up. The full script:

local DataStore = game:GetService("DataStoreService"):GetDataStore("Cash")
function Try10(Func) --Tries to perform Func up to 10 times, returning the results of pcall
	local success, message
	for i = 1, 10 do
		success, message = pcall(Func)
		if success then return success, message end
		wait(0.1)
	end
	return success, message
end
game.Players.PlayerAdded:connect(function(player)
	local key = "user_" ..player.userid
	local v = player:WaitForChild("Value") --I will assume that this 'value' is the Cash Int/NumberValue and that v.Value is the actual amount of cash
	local success, message = Try10(function()
		v.Value = DataStore:GetAsync(key) or 0
	end)
	if not success then warn("Unable to load cash value from datastores: " .. tostring(message)) end
	v.Changed:connect(function()
		local success, message = Try10(function()
			DataStore:UpdateAsync(key, function(oldValue)
				if oldValue == v.Value then return end --returning nil cancels the update
				return v.Value
			end)
		end)
		if not success then warn("Unable to save cash value to datastores: " .. tostring(message)) end
	end)
end)