DS Lite does not use micro switches so the buttons feel mushy.
DSi has micro switches so the buttons are clicky.
I really prefer my DSi. I only use my DS lite to dump and inject GBA saves.
I actually really like the soft feel of the DS Lite buttons, I wouldn't call them mushy though.
Hmmm are there Gameboy carts like the R4 that works with the DS Lite? Because it'd be awesome having DS games pirated and GBA games pirated.
-EDIT-
At the same time, DSi XL sounds pretty good. Might go for that instead since I can already emulate GBA on my phone
There sure are, either the EZFlash 3-in-1 or EZFlash IV Lite Deluxe will do the job nicely. The 3-in-1 uses your DS cart as storage, and when you select a GBA game from the DS flashcart it'll be copied to the slot-2 temporarily (just takes a few seconds if the game is 16MB or less, 32MB games like Mother 3 need to be flashed to NOR which takes longer but is persistent so you don't have to reflash it every time if you're just playing the same game)
The EZIV works similarly, but has its own menu and Mini/MicroSD slot. Recently there was a MicroSD version of the EZIV released but I think it was only released in GBA size.
These are both DS Lite sized so they don't stick out of the bottom.
I believe it's still possible to get ahold of both of them.
Any other GBA flashcart might be tricky to find, there are some other good ones like EverDrive which you can still find as it was released recently (but it's bigger than GBA size so it sticks out a lot on a DS Lite) or M3 Perfect Lite (best option if you can find one but they haven't been in production for ages)
Out of these, the EZ3-in-1 and EZIV don't have RTC, this isn't a big deal but may be annoying in Pokemon as the clock will only progress when you're playing (by use of a clock patch, without that it won't progress at all)
The EverDrive and M3 Perfect Lite do but as said the EverDrive is bulky (not to mention expensive) and the M3 Perfect Lite may be impossible to find.