When it comes to speakers, there are a number of factors that affect the resulting volume. These include power handling, efficiency, impendence (ohms), preferred cabinet design, and frequency range.
The number of watts a speaker can handle is more a measure of power ability than volume. Running 100 watts into a 75 watt speaker will likely result in less than desirable sound, and perhaps speaker damage. A speaker than handles 200 watts may or may not be, on average, louder than a speaker that handles only 100 watts.
Speaker efficiency, usually referenced in Sound Pressure Level (SPL), is usually a better measure of expected volume. Most SPL measurements are done using a standardized sound input (usually white or pink noise) with 1 Watt of power and measures at 1M on axis with the speaker (and usually cabinet).
A typical speaker cabinet will have a SPL rating of perhaps 96db. However some may be lower, and some considerably higher. Note that the difference between two cabinets that rate 96 and 99db in SPL is a factor of two when it comes to power in watts.
Speaker impedance is also a factor as is cabinet design. Most amps will deliver more power to a 4 ohm speaker than to an 8 ohm speaker. Amp specs are the key thing here, and determine how the pair will perform. The amp drives the speaker, which provides the load. A 4 ohm load will tend to draw more power than an 8 ohm load. A 200 watt speaker does not want more power, it simply can handle more power if provided.
It’s also worthwhile to note that cabinet design is a factor in overall speaker performance. There are many types of cabinet design (open back, closed back, ported, etc). Given the same amp and speakers, the cabinet design can significantly affect the resulting sound. The same speaker may perform differently in different cabinet designs.
Frequency range is also a factor here. Most speakers do not have a flat response, but instead perform differently at different input frequencies. Some may accent the bass area where others midrange or higher frequencies. Matching speaker and cabinet design to the desired range is usually a good thing to consider.
As a number of others have already said, speaker efficiency is the most likely issue here. The owner already stated that the impedance was the same, and likely the same cabinet. He took one speaker out and put a different speaker in. He seemed to notice lower volume. My guess is that the original speaker has a noticeable higher SPL rating than the new higher power-handling speaker.
Ed