This one is not exactly for iOS as the apps are mainly for Android mobile phone and TV box, just put it here as well. For iOS, you may have to switch to China region for the two apps not available.
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Karaoke apps
WeSing 全民K歌 (available for iOS)
AngelSing 天籁K歌
ChangBa 唱吧
Duochang 多唱 (available for iOS), take note Duochang mobile version is only for their Karaoke system. Duochang TV version is independent of HW system.
全民K歌 WeSing
VIP for 12 months : RMB 240, or RMB 60 for 3 months, RMB 20 for 1 month.
唱吧 Changba
VIP for 12 month RMB 150, or RMB 20 per month.
天籁K歌 Angel Sing
VIP for 12 months : RMB 198, or RMB 30 for a month.
多唱 DuoChang
VIP for 12 month RMB99, or RMB 20 for one month
Tried a few apps on the Mi Box S and my Android TV box OEM S905X2 TX5 Max, it seems to me 唱吧 is the best. I am using the free version now but I may pay the VIP once my AngelSing VIP expires in three months time.
I have got three months of VIP for AngelSing天籁K歌 and one year VIP for DuoChang 多唱 (RMB99) on the TV box and they are not as good.
WeSing 全民K歌 now does not seem to support 原唱 so it is not good either even though it seems to have the best features and the best contents.
So it depends on what you need. If you need the best contents, probably QQ Music VIP may be the best followed by WeSing. Feature wise Changba seems to be the best but you may not be able to find some songs. This is especially true on the mobile phone side where Tencent probably assets its copyright more closely.
Just an example, I searched 情意结 by Priscilla Chan 陈慧娴 and there is no this song in Changba and AngelSing. Only WeSing and DuoChang have it.
BTW you may need to pay seperately for TV box and phone.