Like KYODE said you can get up to 2150+ from a 35 Remington with out a problem in a G1 Contender with 14" barrel. Probably with H322 powder.
The 357 Maximum with 14 inch barrel and the same 180 grain bullet seated long will go 1850 - 1950 fps. I have broke 2000 fps with 180 XTP's, and H110, but the load was too warm for a G1 Contender in my opinion. I backed my load down to 21.0 grains of H110 and a 180 XTP seated in the lower crimp groove. That is about an 1850 fps load from my pistol. I have a 13" MGM Contender barrel and a CVA Scout rechambered to 357 Maximum. Both are throated to take the 180 XTP's seated in the lower crimp groove. The Scout should take a steady diet of the 1950 fps loads without hurting the gun. I would be a little more cautious with a G1 Contender. The warmer loads may loosen primer pockets a little early also. My initial load development was with Jamerson Brass. I loosened up some primer pockets working up loads. No primer pocket issues with Remington and Starline Brass.
So depending on just how hot you load them, the 35 Remington will go about 200-250 fps faster than a 357 Maximum when both are hand loaded to their maximum potential.
With no 180 SSP bullets, your choices are a little limited on what bullet will perform best at handgun speed. You have the 158 XTP-FP and 180 XTP. Both should work fine, they just shed speed at extended range a little quickly. The 140 FTX will probably be going faster than they need to on impact from the 357 Maximum when pushed to maximum doable velocity. They did not group as well as 180 XTP's in my Scout 357 Max either. I could keep them on a 7" paper plate at 100 yards, but not in a cluster. That leaves the 200 grain FTX. They have a better looking profile than the XTP's. So far I have not tried them in my 35 Bullberry. They are rated to work down to 1800 fps. They have been used with success in a 357 Maximum, but would probably work better going a little faster in a 35 Remington.
180 XTP: Shooting White Tail Deer inside of 150 yards the 180 XTP should work very well in either the 357 Maximum or 35 Remington. With a 150 yard Zero I might try and go a little further with them.
158 XTP-FP: Shooting White Tail Deer inside of 150 yards the 158 XTP-FP should work fine in the 357 Maximum. I would be a little concerned on close shots from a 35 Remington at maximum load speed. Like above I might go a little further with a 150 yard Zero.
200 FTX: Shooting White Tail Deer I would want to keep my shots at 100 yards an under from a 357 Maximum to count on getting any expansion. I would think 200 yard shots with a 35 Remington would get expansion.
Shot placement is everything. You can make killing shots with bullets that do not expand well. Deer are easier to find with a good blood trail from a bullet that expanded, and went completely through however. My shot of choice is a broadside Double Lung Shot that did not touch a shoulder. Less meat loss.
Good luck with your load development.
See You At The Range