They are really very different rifles. I've had the older T3 lite in the past and currently have a Tikka CTR. I've had one of the EW's 8-9 years now. I ran across the EW used in 308 at a good price and hunted with it as is the 1st season or 2. I liked it, but didn't love it. Someone placed a used Edge stock up for sale here in the Classifieds and after putting that stock on it the EW has become my go-to rifle. The factory stock is a good one, but is heavier and thicker than I like. The Edge stock isn't just trimmer feeling, it is 7 oz lighter. The newer EW stock is no different other than color.
Right now my EW weighs 7.5 lbs with a Zeiss Conquest in Talley Lightweight mounts. I think that is a good balance between being light enough to carry, yet still enough heft to shoot well. Mine is consistently accurate with any bullet I've tried in it. Personally I like the more traditional looks of the EW even in SS/Synthetic. I like the CRF action and Winchester safety.
The Tikka is a modernistic looking rifle that will be over a pound lighter than an out of the box EW. It will still be almost 1/2 lb lighter than my EW with the Edge stock on it. Based on my experience the odds of getting an extremely accurate Tikka are a little better. But I doubt I'd be disappointed in an EW. I don't necessarily dislike detachable magazines,but the Tikka mags are more expensive than they should be. Standard mags are 3+1, but in standard calibers 5+1 is available although the 5 round mags do protrude below the stock a bit. The Winchester is 5+1 with a floorplate which I just like a little better.
I like my rifle EW up the way it is better. But the rifles are more expensive then the added costs of a replacement stock will about double what an out of the box Tikka will cost. If I were going to use it as it came out of the box I'd probably buy the Tikka. You really need to handle some of both to decide.