Nevermind, I dumped Proxmox and installed DSM 7 as bare metal because disk write performance was also poor with Proxmox. Now everything is flying, net speed 950 Mbit/s both up and down, USB3 external HDD write 130 MB/s. It might be my HW which is very weak, maybe it would work better on good HW.
In case somebody encounters the same issue, I figured out a solution to get much better network speed using Virtio. You need to disable tx checksumming on the tap interface that Proxmox creates before it starts the VM. For VM 101, command would be: ethtool -K tap101i0 tx off. Problem is that it will work only until you reboot VM, then you need to do it again. Solution for that is to use a simple hookscript in VM config that I made:
#!/bin/bash
# Exmple hook script for PVE guests (hookscript config option)
# You can set this via pct/qm with
# pct set <vmid> -hookscript <volume-id>
# qm set <vmid> -hookscript <volume-id>
# where <volume-id> has to be an executable file in the snippets folder
# of any storage with directories e.g.:
# qm set 100 -hookscript local:snippets/hookscript.pl
# First argument is the vmid
# Second argument is the phase
if [ $2 == "post-start" ];
then
sleep 30
/usr/sbin/ethtool -K tap$1i0 tx off > /dev/null
fi