Obtunded's rather snippy remark aside, there is, potentially, considerable difference depending upon what Shilen barrel you buy and on the luck of the draw.
If you buy a Shilen select match barrel, the barrel is garanteed to be within certain specs. It is hand lapped, gauged, and you are assured of it's dimension. Shilen's standard match grade barrel is a similar barrel but held to less stringent requirements, dimensionally. Still, those dimensions are garanteed.
Now, the McGowan barrel is a well made barrel and the methodology is sound but they don't employ the same gauging and inspection procedures as Shilen. They do a good job of drilling and reaming and they lap prior to rifling. They button rifle and the barrel is turned at the correct rate for the twist during the procedure. My observation has been that they do not actually lap but polish. Their stress relief system is good and their barrels do not warp or move when contoured.
All in all, I would say the best barrels from either maker would be equal. The worst from Shilen would be much better than the worst from McGowan. Shilen garantees the dimensional uniformity of their product; McGowan is pretty sure their's is fine.
The guys at the McGowan shop have been making barrels for about 5 years or so. Shilen has been at it for over forty years.
Shilen's select match barrels are probably equal to any and when you buy one, you know what you are getting. Shilen's standard match grade barrels are very close to as good (I've had some superb chromoly, match grade barrels from Shilen) and, again, you know what you are getting.
McGowan's barrels are a very good standard grade barrel with a little more variability than Shilen's. I think the guys at the McGowan shop are producing a barrel which represents good value. In other words, it's a respectable barrel at a good price. I've been absolutely pleased with the McGowans as a hunting rifle barrel but would choose the Shilen every time for a precision rifle if the choice was between the two.
Because I have no axe to grind either way, I don't have to reflexively slam any barrel because of the method of manufacture or because I don't sell that particular make. A good barrel is a good barrel and a bad barrel sucks; regardless of how it was made or by whom.
I have installed barrels made by at least a couple of dozen different manufacturers. For myself, I would be happy to use a barrel from Hart, Krieger, Pac-nor, or Shilen for a precision rifle. I might try a McGowan for the same purpose but I would do so knowing there was a chance it wouldn't be at the same level. Regards, Bill