With the break removed and a can attached, how much increase in felt recoil is there?

Lots of variables here, but any weight to the rifle should offset felt recoil (unless the suppressor lets additional powder burn under pressure, which could also be a factor).

What loading?  What weight and how many grains of powder?
How heavy is the rifle including optics, mounts, &c.?
Bolt action or ...?
What length of barrel?
What type, including length and weight, is the suppressor?
What position are you shooting from?
What is the delta between your ideal LOP and the fit with the rifle's stock?

Holy over think Batman....

Lets just say same gun, same load, same everything., remove the brake and screw on a suppressor.

What rifle and break?  Not all breaks are created equal.

I am not sure about shooting braked, but my 338 with 27" m24 barrel and McMillan stock feels about like a hunting 308 when I shoot with an AAC Titan

You'll see recoil similar to a .243-.308 rifle with bare muzzle.

I shoot a 338 Edge with a Thunder Beast 338 P supressor.  The Brake on the rifle when not supressed is a Center Shot Rifles Muscle brake, which is an extremely effective brake.  One thing I have noticed on high capacity cartridges and supressors is that the recoil is different in nature.  With the brake there is muzzle rise when suppressed there is zero muzzle rise and all recoil is linear.  I can see bullet impacts at virtually any range with the supressor.  With the brake this is not the case.  Due to lack muzzle rise with the can, perception is that there is less recoil than with the brake.  It would be safe to say that recoil with the can will be conparable to the same rifle with a decent brake.
 

Thanks safetyoff. My buddy has the savage .338lm with the factory brake and i think a 26" barrel. He is just exploring the idea of getting a suppressor for it. He and I both have multiple cans for other guns, but they are all low recoil guns so there isn't any way to really judge from what we have.

Another consideration would obviously be noise, both perceived by the shooter and of those around the shooter. would a large bore gun like a .338 be effectively suppressed to hearing safe levels?

I only have experience with the Thunderbeast can on 338s.  The big 338s are suppressed exceptionally well with this can. The first time I shot it I was very suprised. My perception is that it is quieter than my 280 Ackley or 6.5-284 with a standard 30 cal thunderbeast can and they are quiet.  I can't say hearing safe because I do not know the actual DB level and I still shoot with earvpro usually.  But when I do shoot without ear pro is is far from uncomfortable.  An 308 autoloader with an AAC SDN-6 or Surefire SOCOM without ear pro is uncomfortable for me. The 338 is a level quieter than these.

 
 

Taking off the brake from any center fire rifle and replacing it with a silencer is going to make it much more comfortable to shoot; except for an M1 carbine.

Randy