Upsides to the Blaser;
-Easy as can be barrel change...both accurate and fast both barrel and bolt head/magazine
-Several stock options for both wood and synthetic
-Several scope mounts...fixed,quick change,ring height, rail, red dots.....
-Can add easy to install/remove kickstop
-Easy to pack for travel
-Lots of caliber choices....the newer R8 is adding some big bore/DG calibers as well
-Shorter overall due to magazine layout over trigger(which also tend to be crisp)
Downsides;
-Some can't get used to the strait pull bolt and are just ingrained with the lift of a "regular" bolt
-As Dom said it can be pricey.....but often used components are very well cared for and are just drop in fits always. They hold their value OK, but you do save a bit searching out used market
-Not too much after market components around. Barrels are a factory only deal (as well as bolts and heads)......but there are other manufacturers doing some after market items for stocks/trim/optic mounts.
Overall I have one for two reasons;
-It's an awesome travel gun; compact and discreet.
-I'm not near the rifle looney as most and my Blaser(R93) does just about all of my hunting fun. So I like the consistant trigger/action style between calibers swaps, light and easy to carry all day.