A couple of more points. Simply changing the speakers and not the amp could prove to be dangerous. There is in audio a phenomenon called "clipping". Simply put, if you match a speaker with an amp that has too little power, the amp is unable to control the movement of the speaker back and forth. In a power demanding situation the amp will do a push but be unable to do the return pull. When this happens the current will change from a.c. to d.c. and you end up with a burned out speaker. This most commonly happens to woofers. You have to be careful what you match together. Consult a professional if you are not experienced in this.
In theory a larger woofer should produce better bass because it can move more air. But size is only one factor. What is (in my and other audiophiles opinions) more important is the degree of control that the woofer has. This is largely affected by several factors with the magnet size being one. Where space is a premium, such as in an Elio, I would look for a woofer with a small diameter but a large, heavy magnet. There is no guarantee it will have good sound but a least it's a place to start. Your ears should make the final decision.
Installing a "matched" system from one manufacturer can have the advantage of taking some of the decision making off of you. The manufacturer has already chosen components that work well together. Remember, as with most things, you get what you pay for. Buy a cheap system and you get crappy sound. But quality, you pay more, but it's well worth it.
Finally, most people don't have a clue how to judge a good stereo. They think the one that booms the bass most and plays the loudest is the best. Not true! If you're auditioning a system try listening to it with the bass turned down and see what you think of the sound. Most music is mainly mid-range and you want it to sound natural. If you're please with the sound that way then check out the bass.