I have a Remington 700 in 7mm 08 and I use high rings. I am wondering should I get a 20min scope mounts to shoot high power matches.I will probably be using a Sightron 6x25

Not only yhe3s but hell yes. It will keep you out of the upper end of your scope adjustment.

The rear bridge on 700's is about .020 low. Shim the rear base...and unless you're going after 1000 yd you'll have plenty of adjustment. Always lap your rings. That said ...I like Davidson bases and two screw rings

I have gad to shim every rifle I have except the one with the 20 minute base.

I had to put a 20 minute base on my Stolle to reach 600....the original dove tail had enough for 500 meters (barely) but the extra 8 clicks for 600 were a no-go. A 20 min base has the added benefit of putting the usable adjustment range in the 'middle' of the turret

Any downside to Burris Signature rings with inserts?

Weight. Lap in all rings and do not 'farmer' tighten on the scope