I don't have an R4, so I'll go with what I hear. I have an EzV though, and I don't complain.
R4:
-Pros
Most people have em so its easier to find support.
Support is better, they get patches.
They have cheats
Comes with a bit more: USB MicroSD Reader, key chain case
On the fly DLDI patching
-Cons
It's more expensive (compared prices on DX) R4 is $32 (R4 w/ 3-in-1 ~ $52) & EzV is $28 (EzV w/ 3-in-1 = $42)
Requires more support in some cases: Some games need an arm7 fix to work (didn't we want a slot 1 to get away from patching?) but these are usually fixed after the R4 Team releases a new patch.
GUI (opinion based, you have a choice between 3 options on start, not sure what the options were)
Download play is better I beleive
EzV
-Pros
Requires no new firmware patches to get games working (I haven't ran into a new game that doesn't work)
Optional patching to make games perform better (never used it ever though)
Cheaper (compared prices on DX) R4 is $32 (R4 w/ 3-in-1 ~ $52) & EzV is $28 (EzV w/ 3-in-1 = $42)
GUI (1.41 GUI was good, I'm not liking te 1.6+ GUI though)
Integrated Moonshell 1.71 (1.6+ kernel only, 1.41 has Moonshell 1.5 integrated) enabling you to play your videos, mp3s, and read text right away without booting or selecting moonshell (was one reason I got the EzV)
-Cons
Support (was almost gone for like 6 months, but seems like they're back, and even when they were gone there was no problems booting and playing any game, so we almost didn't even need support to play new games.)
Takes longer to boot games (saves are saved on a chip which are written to the MicroSD when you change games, which gives the EzV better compatibility; I figured a couple seconds is better than worrying about decompiling a rom, patching, and recompiling the rom)
No cheats
PCB is exposed (hidden under sticker, if you think about it, it stays in your DS most of the time anyways)
GUI (1.41 GUI was good, I'm not liking te 1.6+ GUI though)
Download play doesn't work for a few games
Homebrew got broken for some apps (most of the major ones weren't affected)
Homebrew requires DLDI patching manually (a front is available to do this easily though)
Kernel 1.41 requires savelists (1.6+ don't require save lists, and autodetects save type)
Other note:
I think the only games on the EzV that aren't supported are those games with those whacky peripherals that are needed to even play those games. I think they boot, but ask you to stick in the peripheral it needs.
I think the big things the R4 has over the EzV is really just download play and cheats. The big thing that I can think of that the EzV has over the R4 is virtually all new releases will work right away, usually someone comes up with a fix for those games that don't work on the R4 (there isn't many, but it happens); can't back this up, but maybe if you look at the patches that are released on the R4, I think a lot of em are game fixes; not saying that they didn't release patches that enhanced the cart itself(if you look at the changelogs from 1.08 - 1.12, they all contain game fixes I think). That's all I can think of for now.