Hitting/Batting
Baseball: The hitter either slogs or slaps an incoming ball. There is no wicket behind him that he needs to worry about. Then he advances by bases unless a home run is hit whence every hitter is allowed to complete the square. That's it. Simple.
Cricket: A batsman plays either defensively or aggressively (or a mix of both) depending on tactical requirements such as the influence of net run rates, skill of the active bowler (pitcher) and placement of certain fielders. The lack of a strike-out concept in Cricket means that a batsman could potentially "hit" for an entire inning and face numerous deliveries!! And all of that while protecting 3 Stumps (or the wicket) and being wary of the wicket keeper right behind him. Shots involve blocks, cuts, drives (cover, square, on), pulls, hooks, scoops, sweeps (regular, paddle, reverse), slogs (baseball style), glances, flicks and the Marillier and are accomplished using the appropriate footwork. Shot selection becomes crucial when a high run-rate is required. In addition, 1 or more runs can be scored against a single delivery. The equal of a home run in baseball provides 6 runs in cricket unless...the ball where to hit the ground at least once before it reaches the boundary, in which case, only 4 runs are provided.
Six consecutive sixes (homeruns)
Pitching/Bowling
Baseball: Mostly full tosses where the pitcher delivers the ball to the strike zone without the ball hitting the ground. The ball may not always take a linear route to the hitter depending on its wear pattern and wind conditions. That's it. Simple. It is not uncommon to use the same pitcher for the entirety of a team's pitching.
Cricket: Bowling can be both defensive and offensive depending on tactical requirements. While the occasional full toss is delivered to a batsman, it is usually done because the bowler slipped up or the bowler decides to surprise the batsman with a different type of delivery. Usually though, bowlers (both pace and spin) deliver so that the ball pitches (hits the ground) atleast once before reaching the striking batsman (inside the strike zone). So a delivery can be a high/low full toss, short ball, length ball or a yorker. The combination of such pitching on the ground, weather (wind and dampness on ground) and wear pattern can make the ball turn or swing in a variety of ways, improve bounce or dampen it and either slow the ball down or speed it up. Because the ball pitches, the condition of the ground laid out between wickets plays a significant part in the toss winning team's decision to bat or bowl first.
So the batsman needs a really quick eye and then has to decide in a fraction of a second as to how to play the incoming ball using the appropriate shot. The bowler could bowl a wide ball or a no-ball and provide a run to the batting team in the process, which can sometimes prove crucial in the later stages of a game. Toward the end of a game, the run up used by a bowler to get to the bowling zone to deliver the ball can work the crowd up and put pressure on batsmen and fielders alike. This I have found to be not nearly as spectacular in baseball.
Fielding
Baseball: Restricted to the square. Fielders use a glove to pick up the ball. I have seen some spectacular catches taken in baseball.
Cricket: The ball can be hit to any corner of the ground by a batsman. Fielders, except the wicket keeper who is always behind the striking batsman, do not wear gloves. Again, I have seen spectacular catches fielding moves made in cricket but without the aid of a mitt or a helmet.
Fielding (no mitt)
Because of the variety of shots that could be played and the bowling styles involved, the Wicket Keeper (fielder behind the batsman) has an athletic role to play in cricket.
Cricket fielding positions
Getting Out
Baseball: The 3 common ways a hitter can be dismissed are Strike outs -- hitter misses playing 3 balls in a row, catches and run outs (before a hitter can reach one of the bases, he is tagged).
Cricket: Bowled out (ball hits the stumps behind batsmans), catches, runouts, LBWs and stumpings are the 5 common ways a batsman can be dismissed. The type of bowling style, pace or spin, in a given situation can be used to predict how a batsman can be dismissed. For instance, stumping of the batsman during spin bowling occurs commonly in a high run-rate requirement situation. So the type of bowlers in the active team are culled from a bigger roster depending on pitch and weather conditions.
Game Format
Baseball: Has only one format comprising of 9 innings for each side.
Cricket: Has three formats. Test cricket is played over 5 days for multiple innings. I never watch it. One-Day International (ODI) cricket is played for around 6 or 7 hours total with one inning for each team with a couple of drink breaks in each inning and a lunch break. I only watch ODIs during the World Cup, which happens every 4 years. The newly invented Twenty20 format lasts for around 2.5 or 3 hours total with one inning for each team with a single (10 minute or so) break. I am really hooked on this format now! Twenty20 games are played in the evenings (local time) and many expect them to completely replace ODIs. The T20 World Cup happens every 2 years.
Wrap-Up
Additionally, in cricket, the team captain is responsible for making all tactical decisions and coaches have no say once play begins. This decision making capability by a player, along with the various batting styles, simply does it for me! For uncontrollable situations, such as rain, the team captains work with in-ground umpires to decide on the fate of the game or adjusting it to fit time and run rate constraints.
The IPL and the art of captaincy
Having said all that, I have to add that two of my favorite movies are The Sandlot (a real favorite) and A League of their Own :)
