What VM host software are you using? If it's VirtualBox, just install the guest additions and use it through there.
RDP is really a Microsoft-only protocol. It's better on Windows than VNC because AFAIK it's just sending draw calls across the wire. I'm not sure what XRDP does.
You may actually have a better experience on a Pi 2 or 3, because of the way Raspbian is set up to run by default.
TeamViewer has a native linux build, which works well: https://www.teamviewer.com/en/download/linux/
Not sure why you'd want to use Wine.
I could also have used VNC but I much prefer the RDP experience, in particular being able to share the clipboard with the local machine and to copy text and files.
VirtualBox also does clipboard and file sharing, but only with the Guest Additions (only tested under a recent Ubuntu).