Some quick thoughts:
15" LCD is roughly the same viewable size as a 17" CRT.
A 15" LCDs MAX/native rez is prolly 1024X 768. First-gen may even have a MAX/native of 800 x 600
Most LCDs don't support any freq. higher than 60 or 65 hz.
Key factor to LCD "performance" with twitch games and/or fast video = pixel recharge rate.
Even with the best rates...the LCD may show bleed in games and movies.
Post the EXACT model of LCD for a more detailed assessment.
From what little we know now, I'd suggest stickin with your 21" CRT, unless you plan to use the 15" LCD as a secondary monitor, and buy a BETTER 21" CRT as primary.