Possible spoilers within, but just to elaborate on the different modes a bit without filling up the discussion thread in Shmups Chat...
Arcade mode is the arcade game. No differences that I've noticed so far.
Grabbing and throwing enemies has both an offensive/defensive component and a scoring component. Enemies thrown into other enemies are extraordinarily damaging, and even if a throw fails to destroy an airborne enemy, it will often knock it clear of the screen. Enemies thrown will also cancel bullets along the path of the toss.
Destroying enemies and absorbing bullets with captured enemies releases small medals, which can be grown into large medals by holding the shot. Tossing enemies into other enemies releases larger medals. Destroying large enemies and boss forms turns all bullets onscreen into small medals. Larger medals with increase both your medal count and your score multiplier more than smaller medals.
Medals increase the multipler, while using captured enemies to destroy other enemies "cashes in", decreasing the multiplier in exchange for points and a quantity of large medals. An exception is during boss fights, where an enemy captured before the current stage of a battle can be tossed with no detrimental effect on multiplier.
V.B.A.S. system is basically set up so that when you destroy one lifebar of a boss, your current number of medals determines whether you move to the next form or destroy the boss. If you have enough medals after you destroy the last boss form in Stages 1 and 3, you'll fight Faintear. When you die, your medal count is reduced (to 3/4? 2/3?)
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Story mode is, stage and score-system wise, identical to the arcade game. However, unlike Arcade mode where you will only encounter Faintear if you've medalled enough to earn it, you'll always run into her at the end of Stage 1 and Stage 3 in Story mode. She's also fought again before the final boss, unlike in the Arcade mode. This is probably the reason for the different score tables.
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Arrange mode uses the same basic play system, but turns the score system around to make heavy grab-n-toss gameplay very profitable and more difficult. Enemies shoot approximately 3 times as many bullets, and certain patterns have changed to make dodging more difficult. The multiplier is gone, but medals gain value much more quickly. It's no problem to finish Stage 1 with over 75000 medals collected. The more medals you have, the more points you earn by destroying things by tossing other things into them... the more you toss things into other things, the more medals you earn. However, the durability of captured enemies is severely reduced due to the large number of additional bullets on screen.
Worth noting, in the Arcade/Story modes there is a smooth and moderate slowdown that occurs during large explosions, creation of lots of medals, or cancellation of lots of bullets. Times when there's probably nothing you need to be worried about getting out of the way of.
In the Arrange mode, the game will slow down more frequently due to the denser patterns (good thing?) but will occasionally return to normal speed basically without warning (very bad).
