Yes and no. Here's a limited comparison:
Civ IV with BtS
-Music through the ages (all European though)
-Graphics are cartoony-esque, but the wonder animations are nice (esp. Statute of Zeus)
-More complexity (esp. with diplomacy--UN, temporary alliances, etc)
-Combat is more complex and has less micromanagement, but also takes way longer to wage successfully. Collateral damage and flanking function nicely.
-Expressive leaderheads, with memorable, but simplistic, music, and more depth as far as trading screens, etc
-Religion is more culturally specific (i.e. Hindu missionaries looking like Gandhi)
-Expanded builder options (espionage is expansive, if too complicated for its own good, UN, diplomatic random events/quests, trading posts level up by turn rather than by age, Great People can do more things)
-Squares (move diagonally--it's faster).
-Can move huge stacks of units with two clicks.
-UI is terrible, but allows you to access almost any info with one click (victory progress, religion, etc)
-Can take over cities with riots and culture. Policies don't require culture to unlock, just tech progress
-Tech tree more complex and strategic. Also, bonuses for being first to research a tech, etc.
-Multiplayer actually works. And is fun. Also, PitBoss.
-Shorter loading times.
-Leonard Nimoy voice-overs.
Civ V w/ GnK:
-Music for each area (limited in scope, however)
-Improved graphics (clouds, mountains, shining water)
-AI are inane diplomatically (you were my friend from across the sea 30 turns ago...NOW DIE)
-Combat is simpler, and imo more satisfying (also cities can defend themselves without having units stationed in them)
-Animated leader screens, with great music.
-Religious customization (bonuses, etc)
-Limited peacenik/builder options (can't build anything but plantation on area with bananas)
-City-state diplomacy is mediocre, but adds some flavor now with espionage
-Hexes
-Unit control is more annoying and micromanagement focused
-UI is simpler, cleaner, nicer-looking, but less functional (have to click in each game to have the building queue show, also accessing victory info requires multiple clicks, and the diplomatic relations screens are annoyingly unorganized)
-Victory conditions are limited, but the combat victory no longer requires taking every-single-city.
-Can't take over cities via culture/riots/etc. Culture required to unlock policies, which means a really combative player may get his next policy unlocked in 48 turns. Enjoy the wait.
-Tech trees simpler (tech line above = culture/exploration/navy, mid-line tech = economy, tech line below = combat)
-Scenarios are more pithy and combative (see Fall of Rome for example). Scenarios include lines from Pirates of the Caribbean and other such, voiced by a Star Trek actor that is not Nimoy.
Bottom Line:
In short, Civ IV BtS is the nuclear scientist to Civ V's college graduate with BA in science. The nuclear scientist is more arcane, harder to understand, but more valuable mentally. The college graduate degree is functional, but limited--and more accessible as a result. Personally, I play both depending on how long I want my games to be (Civ V's end game is much more tedious than Civ IV's end-game, however).