Not sure if you have sorted this out yet but I would just transfer the emails between accounts with with IMAP. All the email servers can use IMAP so it shouldn't be and issue to do that.
I'm assuming that 1) you are using the default "Windows Mail" program in Vista (and not Windows Live mail, which is now defunct, but even if it is WLM the same procedure listed below should work with that program also)..."Windows Mail" was the successor to Outlook Express,
and 2) that you were using POP3 and not IMAP on the Vista machine, which is why all your old emails reside on your Vista machine. I'm additionally assuming that your Vista machine is still functional and you are able to open Windows Mail.
Now a couple of quick questions:
On you new Windows 10 machine, are you using the Win10 default mail app? If so do you have a new email address that you are using with it, or are you still using you old email that you were using on the Vista machine with Windows Mail?
If you are using the same email address as before then I am guessing that it is now probably configured as an IMAP account on the new machine (as opposed to POP3 on Vista). If that is the case, then all you will need to do is reconfigure the Vista Windows Mail account to use IMAP(vs. POP3) on that machine. Once you have done that then all you will need to do is move (or copy) the email from the Local Inbox/Folders in Windows Mail to the new folders under the newly configured IMAP account, which should be showing now in the "tree" below the Local Inbox/folders.
If you are using a different email account on the new machine , the same basic idea still applies. Create a NEW IMAP account on the Vista machine in Windows Mail (You can have multiple accounts in Windows Mail) with the same server/credentials you are using on the new machine. Once you have done that, then again all you have to do is copy/move emails from the Local Inbox/folders to the new IMAP account you created. If you have a lot of emails, it could take a while to transfer (and it will first have to upload to the server, then be pulled back down to the new client on the new machine).
I move email like this all the time between various accounts (aol, yahoo, gmail, etc) and it works well...
Hope this helps - it really isn't very hard or complicated.