I'm going to respond here, because that other thread didn't mention the eWin 2in1 which in my opinion has some advantages over the EZ 3in1 (besides being cheaper). I also think that the other thread muddies the water by mentioning other slot2 carts that aren't really what ShinKyo is looking for (a simple GBA expansion cart). The two best-supported GBA expansion carts are the EZ 3in1 and the eWin 2in1.
At $14 shipped (from psxboy.com) the eWin 2in1 doesn't have rumble (that's why it's a 2in1 instead of a 3in1). It will play GBA games and it will work as extra memory needed by the Opera browser, just like the EZ 3in1. If you really want rumble (you think you want it, but you don't really want rumble, trust me) you'd have to buy a separate rumble pack for around $4. If you must have rumble (you don't really want it) the eWin rumble pack is actually better than the EZ 3in1's built-in rumble. But you don't really want rumble. Really, you don't. Rumble doesn't work for GBA games and only a few NDS games support it, it eats up battery, and it's not particularly "rumbly." Also in some cases, the rumble will apparently start rumbling for games that don't support rumble and in some cases it won't stop until you shut off the DS. Did I mention that you don't really want rumble?
As for playing GBA games (which after all is what these carts are really designed for), the EZ 3in1 has two types of memory: faster volatile memory (it can only store a game while the power is on) and slow NOR flash memory (it can store a game while the power is off). With the NOR memory you can store a game and then you can play the game as many times as you want without reloading it. The problem is that a game will take 1 to 2 minutes to store to the NOR (whereas the faster memory only takes a few seconds) so I'm not really sure why you'd want to use the NOR. Except that you have to use the slow NOR memory for larger GBA games (there isn't enough of the fast volatile memory to store large games). In all fairness, the NOR memory runs a game much faster than it stores it, so once it's stored onto the NOR, you can play it many times fast. I just don't think it's worth the trouble to avoid waiting a few seconds to load your GBA game to the faster memory (and you have no choice for larger games).
The eWin 2in1 has more of the faster memory than the EZ 3in1 -- enough to load the largest GBA game -- but no NOR memory. Because you don't have to mess with NOR memory, the eWin is easier to use.
Note that you'll need the GBA ExpLoader program to use either the EZ 3in1 or the eWin 2in1 with your R4. Get the latest version of GBA ExpLoader here:
http://kotei.blog.so-net.ne.jp/archive/c530-1
-Bri