In short, I'd tell him to to be afraid of new technologies and moving in the way of the furture - open source. However, I don't need to worry about keeping that job. To get the things your coworker is talking about you'd need to ditch Dreamhost and find a microsoft server.
In more detail...
If you were working directly with the same type of database things would be easier. Instead of having to worry about converintg between two types, making sure data types are compatable - I can see it would save a lot of headahces to be using the same setup on a local box and the server. You could consider working directly with mysql so there's no conversion issues, but you'll have to figure out if that's worth the investement of time in the long run.
I also think that mysql is far more secure tha ms-sql. Mysql is actually password protected, and at dreamhost is stored on an other server entirley. That means that if you end up with an un-secure script on your account, file access to your account doesn't mean you'r database has been comprimised too.
As far as PPTP and VPN goes, I'm not sure that you need it really. You can get VPN access at Dreamhost with the Stricly Business plan - But what do you need it for really?
As far as ASP goes, the only chance of having that work at dreamhost would be with a dedicated box. There's a program called mono that you can use as with mod_mono for apache support, or by using their own server, XSP to server ASP files. If you're using it mod_mono and apache then any file with an extension of .asp would be parsed through mono before being set out. Unfortunalty this system can't be run through Dreamhost shared hosting.
Is ASP better than PHP, or is it that special? That one is a really complicated question. There's a lot of discussion on the internet about that one - and you can go a google serach to find it. My personal opinion is that ASP sucks, isn't stable, and will be going the way of the dinosaur soon. ASP sites that I'm familiar with have frequenly planed site-wide down times for 'maintance'. The local community college here uses all microsoft servers for their registration stuff, and they only have the system aviable between 8am and 10 pm - it needs bueatly sleep or somehting. So if I need ot check my class schedule or grades I have to access the system between thoes hours. that really sucks. linux and PHP can run 24/7.
This entire discussion basically boils down to is Microsoft or Linux better. And there's all sorts of factors and propaganda out there. You'll have to decide what's best for your situation. How much does hosting cost you at dreamhost. How much will it cost on a micro$oft server? How much time will it take to convert eveything over to work on the new server? How much time will it take to re-train your coworker to use linux? Will there be a difference in the way your emploies access the system, and is one way more convient for them? All of these questions and more may influence your decision.
I'd try and sort things out, see if you can come up with a clear decision, of one way is cheeper or better... or just see who has the strongest will or best influence with the boss.
Hope this was helpful.