Just to rule out the case of bad compatibility between the STA on the router (Quantenna QSR1000 chipset, QT3840BC SoC in case of my RT-87U) and the client WNIC I also checked with a different STA.

So the second router's 802.11ac hardware is Compex_WLE900VX Qualcomm Atheros QCA9880 (V2) which uses ath10k driver as well. Therefore, I've tested laptop's ath10k on 4.10 with router's ath10k on 4.4 kernel:

root@turris:~# uname -r
4.4.39-80079e1c1e5f9ca7ad734044462a761a-4 

root@turris:~# lspci -vvv

02:00.0 Network controller: Qualcomm Atheros QCA986x/988x 802.11ac Wireless Network Adapter
	Control: I/O- Mem+ BusMaster+ SpecCycle- MemWINV- VGASnoop- ParErr+ Stepping- SERR+ FastB2B- DisINTx+
	Status: Cap+ 66MHz- UDF- FastB2B- ParErr- DEVSEL=fast >TAbort- <TAbort- <MAbort- >SERR- <PERR- INTx-
	Latency: 0, Cache Line Size: 64 bytes
	Interrupt: pin A routed to IRQ 120
	Region 0: Memory at e0200000 (64-bit, non-prefetchable) [size=2M]
	Expansion ROM at e0400000 [disabled] [size=64K]
	Capabilities: [40] Power Management version 2
		Flags: PMEClk- DSI- D1+ D2+ AuxCurrent=375mA PME(D0-,D1-,D2-,D3hot-,D3cold-)
		Status: D0 NoSoftRst- PME-Enable- DSel=0 DScale=0 PME-
	Capabilities: [50] MSI: Enable+ Count=1/8 Maskable+ 64bit-
		Address: f1020a04  Data: 0f10
		Masking: 00fe00fe  Pending: 00000000
	Capabilities: [70] Express (v2) Endpoint, MSI 00
		DevCap:	MaxPayload 256 bytes, PhantFunc 0, Latency L0s unlimited, L1 <64us
			ExtTag- AttnBtn- AttnInd- PwrInd- RBE+ FLReset- SlotPowerLimit 0.000W
		DevCtl:	Report errors: Correctable- Non-Fatal- Fatal- Unsupported-
			RlxdOrd+ ExtTag- PhantFunc- AuxPwr- NoSnoop-
			MaxPayload 128 bytes, MaxReadReq 512 bytes
		DevSta:	CorrErr+ UncorrErr- FatalErr- UnsuppReq- AuxPwr- TransPend-
		LnkCap:	Port #0, Speed 2.5GT/s, Width x1, ASPM L0s L1, Exit Latency L0s <4us, L1 <64us
			ClockPM- Surprise- LLActRep- BwNot- ASPMOptComp-
		LnkCtl:	ASPM Disabled; RCB 64 bytes Disabled- CommClk-
			ExtSynch- ClockPM- AutWidDis- BWInt- AutBWInt-
		LnkSta:	Speed 2.5GT/s, Width x1, TrErr- Train- SlotClk+ DLActive- BWMgmt- ABWMgmt-
		DevCap2: Completion Timeout: Not Supported, TimeoutDis+, LTR-, OBFF Not Supported
		DevCtl2: Completion Timeout: 50us to 50ms, TimeoutDis-, LTR-, OBFF Disabled
		LnkCtl2: Target Link Speed: 2.5GT/s, EnterCompliance- SpeedDis-
			 Transmit Margin: Normal Operating Range, EnterModifiedCompliance- ComplianceSOS-
			 Compliance De-emphasis: -6dB
		LnkSta2: Current De-emphasis Level: -6dB, EqualizationComplete-, EqualizationPhase1-
			 EqualizationPhase2-, EqualizationPhase3-, LinkEqualizationRequest-
	Capabilities: [100 v1] Advanced Error Reporting
		UESta:	DLP- SDES- TLP- FCP- CmpltTO- CmpltAbrt- UnxCmplt- RxOF- MalfTLP- ECRC- UnsupReq- ACSViol-
		UEMsk:	DLP- SDES- TLP- FCP- CmpltTO- CmpltAbrt- UnxCmplt- RxOF- MalfTLP- ECRC- UnsupReq- ACSViol-
		UESvrt:	DLP+ SDES+ TLP- FCP+ CmpltTO- CmpltAbrt- UnxCmplt- RxOF+ MalfTLP+ ECRC- UnsupReq- ACSViol-
		CESta:	RxErr- BadTLP- BadDLLP- Rollover- Timeout- NonFatalErr-
		CEMsk:	RxErr- BadTLP- BadDLLP- Rollover- Timeout- NonFatalErr+
		AERCap:	First Error Pointer: 00, GenCap- CGenEn- ChkCap- ChkEn-
	Capabilities: [140 v1] Virtual Channel
		Caps:	LPEVC=0 RefClk=100ns PATEntryBits=1
		Arb:	Fixed- WRR32- WRR64- WRR128-
		Ctrl:	ArbSelect=Fixed
		Status:	InProgress-
		VC0:	Caps:	PATOffset=00 MaxTimeSlots=1 RejSnoopTrans-
			Arb:	Fixed- WRR32- WRR64- WRR128- TWRR128- WRR256-
			Ctrl:	Enable+ ID=0 ArbSelect=Fixed TC/VC=ff
			Status:	NegoPending- InProgress-
	Capabilities: [160 v1] Device Serial Number 00-00-00-00-00-00-00-00
	Kernel driver in use: ath10k_pci


root@turris:~# iperf -s
------------------------------------------------------------
Server listening on TCP port 5001
TCP window size: 85.3 KByte (default)
------------------------------------------------------------
[  4] local 192.168.1.1 port 5001 connected with 192.168.1.149 port 45706
[ ID] Interval       Transfer     Bandwidth
[  4]  0.0-10.0 sec  27.4 MBytes  22.9 Mbits/sec

The result is the same so it is definitely not a router/compatibility issue.