NOTES:- Always check the official site for your kit before updating the 3DS to make sure your kit is up to date and works with the latest 3DS update, I am only taking version notes for the SupercardDSTWO kit as that is the one I use myself
The other kits listed are of lower quality made with cheap parts and will require patching of protected games before they will work with those kits but they are cheap, so if you are a new user then be aware of the limitations first before just going for a cheap kit, at the end of the day that is up to each user, there are plenty that are happy with there cheaper flash kits
3DS/2DS version 9.0.0-20x
Working WIP update (I presume it's the same kits again that are still working though, will confirm this soon)
R4i Gold 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
3DS/2DS version 8.0.0-18x/19x
Working
Supercard DSTWO [DSTWO Firmware update 1.25 required]
ACE3DS PLUS
R4i Gold 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
R4iDSN 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
3DS/2DS version 7.1.0-17x
Working
Supercard DSTWO [DSTWO Firmware update 1.25 required]
ACE3DS PLUS
R4i Gold 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
R4iDSN 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
R4i-SDHC 3DS RTS <- homepage unknown to me
R4iSDHC Silver <- homepage unknown to me
R4iSDHC Dual-Core <- homepage unknown to me
R4i-Gold Pro <- homepage unknown to me
3DS/2DS version 7.1.0-16x
Working
Supercard DSTWO [DSTWO Firmware update 1.25 required]
ACE3DS PLUS
R4i Gold 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
R4iDSN 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
R4i-SDHC 3DS RTS <- homepage unknown to me
R4iSDHC Silver <- homepage unknown to me
R4iSDHC Dual-Core <- homepage unknown to me
R4i-Gold Pro <- homepage unknown to me
3DS/2DS version 7.1.0-15x
Working
Supercard DSTWO [DSTWO Firmware update 1.25 required]
ACE3DS PLUS
R4i Gold 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
R4iDSN 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
3DS/2DS version 7.1.0-14x
Working
Supercard DSTWO [DSTWO Firmware update 1.25 required]
ACE3DS PLUS
R4i Gold 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
R4iDSN 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
3DS/2DS version 7.0.0-13x
Working
Supercard DSTWO [DSTWO Firmware update 1.25 required]
ACE3DS PLUS
R4i Gold 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
R4iDSN 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
3DS version 6.3.0-11/12x
Working Flash Kits
Supercard DSTWO [DSTWO Firmware update 1.23 required]
ACE3DS PLUS
R4i Gold 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
R4iDSN 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
3DS version 6.2.0-11/12x
Working Flash Kits
Supercard DSTWO [DSTWO Firmware update 1.21 required]
ACE3DS PLUS
R4i Gold 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
R4iDSN 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
3DS version 6.1.0-11x/6.1.0-12x
Working Flash Kits
Supercard DSTWO [DSTWO Firmware update 1.20 required]
ACE3DS PLUS
R4i Gold 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
R4iDSN 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
3DS version 6.0.0-12x
Working Flash Kits
Supercard DSTWO [DSTWO Firmware update 1.20 required]
ACE3DS PLUS
R4i Gold 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
R4iDSN 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
3DS version 6.0.0-11x
Working Flash Kits
Supercard DSTWO [DSTWO Firmware update 1.20 required]
ACE3DS PLUS
R4i Gold 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
R4iDSN 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
3DS version 5.1.0-11x
Working Flash Kits
Supercard DSTWO [DSTWO Firmware update 1.19 required]
ACE3DS PLUS
R4i Gold 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
R4iDSN 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
3DS version 5.0.0-11x
Working Flash Kits
Supercard DSTWO [DSTWO Firmware update 1.19 required]
ACE3DS PLUS
R4i Gold 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
R4iDSN 3DS revisions 9,A & C (There is more than 1 version of Revision C only one works)
I will update this as the 3DS is updated
Notes....
If you are looking for the best kit then go for the Supercard DSTWO
If you are looking for the cheapest option an R4 will do, it uses a homebrew kernal being WooD
DS rom compat is based on the kernal so 3 of the above listed cards will have the exact same compat as long as the kernal is of the same version
The console compat is based on the flash kits firmware (called a patch by the R4 kits & the Ace3ds) [Ace3ds call the kernal a firmware (no idea why)]
For the Wood kernal you may be required to AP patch some games to make them work, it's not such a big thing but this is the price of going with a cheap card