I don't have a real favorite, civ5 has many improved things, both are quite a different game imho.
First play 4, then later 5.
Imho crappy in 5:
Hex instd. of grid.
No unit stacking ( painfully slow game at the end when you've won already and have an army 5x as large as the AI, but can't finish the game quickly as you have to move 50-100 units per turn 1 by one instead of in 2 or 3 big stacks.
In the beginning, happiness, even if you have all the luxury resources, it's hard to keep it up with growth of your cities if you're a decent micro-manager.
Rest is pretty good imho
Crappy in 4:
(Imho) culture, what you can do with gold, AI only making military... The ''fat cross''/ crappy city working limits, and city maintenance costs.
Then civ5 has the funky new policies system, I've grown fond of ranged combat in civ5, I've grown fond of city states and natural wonders, and also the happiness system ain't bad. Also like the way research & gold are seperated now.
But the no stacking means its boring/slow endgame where you are most powerful but have to go on and on to actually get a victory.
And hex means only 6 directions to go to instead of 9, combat has become FAR easier, especially against a dumb ai, you can pretty much own the AI with an army half as small (that applies to civ4 too I guess with good use of colleteral damage against ''stacks of doom'', but it's got worse, if you have a good chokepoint you can hold a 15 man army with a 3 man army so to speak now).
I never understood the whining about ''stacks of doom'' in civ4, of course you can put a whole army in a tile/hex ( which in reality would be hundreds of square miles) and I don't think it's realistic I can hold off a whole army of 20 (or more!) spear, swordsmen, etc, with 2 swordsmen and a chariot archer.
Endgame in civ5 is simply boring, the beginning is somehow always tough, very tough ( I play at Emperor difficulty level so ai ''cheats''), but near the endgame it's still Modern armor & stealth bombers vs (old) canons and renaissance riflemen. And it's painfully slow when you can't simply stack up 10 modern armor and blitzkrieg to the AI capital but have to slowly move em 1 by one

, and spend 1-2 more hours more on a game from a certain point that should be over in 5-10 minutes.
Civ5 is the only game really which has this problem, in any other strategy game, the moment you really own the ai, have an army 2x as big and modern than the AI, the AI no decent defenses, etc, you throw you army at the enemy easily and end the game in a couple of minutes without too much hassle, civ4 was already slow endgame, civ5 is even WORSE, far worse. I can't remember this problem in games like erm, Rise of Nations, Supcom, Age of empires, Rome total war, Command and conquer, Sins of a Solar Empire, etc... That is the only main flaw imho, even if you're 5x as strong, you still have to spend ages winning the game, rather than just sitting back, throwing an army 5x as big at the enemy or a rally point in the enemy base with all your factories/barracks working, sitting back, and watching the carnage.
Endgame in most strategy games is awesome, carnage, explosions, voilence, easy, etc...
In civ5 ( civ 4 also a little bit, but to a far lesser extent thanks to unit stacking), the end is tiring, ''meh'', and boring. It just goes on and on. Shame, as otherwise both civ4 and 5 are epic games which will always be in my top10 games of all time.