The amperage is the rated power it can handle. Modern houses are generally built with 200 amp panels, and a lot of the newer ones are going 300-350 amps as more and more electronic devices and fancy and high-demand kitchen devices and increased lighting are used in homes.
Both are just as safe - the 200 amp one will just have many more breaker slots, allowing way more circuits, and providing more room for expansion in the future, especially for power-hungry things like shop tools. Each uses only as much electricity as is used in the circuits - the panel itself does not consume any electricity, so no long-term impact there. It is just a circuit connection box where the individual circuits are connected, with circuit protectors (breakers) in line before it connects to the main line to your electric usage meter.
Unless you are real tight on money on this job, I would upgrade to 200 amps capacity - the incremental cost is about $100-200 or so over the 100 amp panel. If your incoming power line cannot handle 200 amps, you could install a 100 amp main breaker to keep the power company happy but put in the 200 amp breaker panel, so in the future a main line upgrade could be done with only a main disconnect breaker upgrade of $100 or so, without having to change anything inside the house.
Having the larger panel, especially if 200 amp capacity all the way from the meter, can be a selling point (or rather, lack of a negative point) to a potential buyer with lots of electronics or who is into shop power tools. It would also facilitate conversion to electric heat / water heating if someone wanted to do that.