The service providers are only targeting illegal downloads through peer-to-peer sharing since those use the bandwidth all the time. Whether you agree with this or not (to me it's like going to an all-you-can-eat buffet with a sleeping blanket, but I sell telco equipment so I kow how much bandwidth costs), typically it's hard to press the point that you're downloading an illegal copy of a movie and not getting the speed you think you should... Comcast is actually the biggest offender here, a few people in the same neighborhood running a BitTorrent client can kill the entire network for all the homes passed, it's a fundamental flaw in the cable system architecture. Verizon isn't as bad in that respect but their wireless unlimited data plan is actually profiled and if it looks like you're violating the TOU by sharing the connection or by running a file server they'll cut you off - the same may be true of FiOS but I haven't heard about it. I also haven't heard of them rate limiting bandwidth from any provider to legitimate servers like iTunes and my BitTorrent downloads (granted, mostly of legitimate files) hasn't been throttled.
I have the 10Mbps service, Verizon is probably making you the offer because they're looking to drop some of the lower bandwidth services (I know my plan isn't currently offered). Various speed tests peg me at a hair over the promised rate both up and down, but more importantly downloading large files from well-known servers seems to be pretty darn close to 10Mbps (remember a lot of programs report MBps, so you'll have to multiply by 8 to get the right value - I use 10 because there's also packet overhead involved and math class was hard

). I'd imagine that iTunes downloads would be much faster, but large numbers of smallish files like photo sharing may or may not be affected depending on which service you use (some require a lot of processing on the server-side between uploads which negates your speed increase). Today's YouTube-type services are fine at 5Mbps, but in the near future you may be able to get streaming HD video from websites like that where 20M would be a benefit.
Also look into their TV service if you haven't already. I've got it and even with standard def (Verizon has issues getting HD set top boxes) it's so far been more reliable than my previous house's cable and better than DirecTV because I've got too many trees to get a good signal - plus it doesn't go away in heavy rains. Verizon has some triple-play (voice/video/Internet) and four-play (add in wireless) deals that can be attractive.