I too changed from a .308. Although I owned it for decades and it did the job, I never loved it. When trying to decide which calibre to plump for, I was looking for less recoil (much less if possible) and something I could love.
I whittled down to:
6.5x55SE Which will lay low anything the UK.
.25-06 Which will lay low anything the UK.
7mm-08 Which will lay low anything the UK.
I chose the 6.5x55SE because it's such a sweetie to shoot, and has such a huge range of bullet weights (although I'll just start with factory 140gr).
Because a lot of SERIOUS and knowing stalkers use the Swede and so much positive press has appeared about it, both here, and in the States, there is an inevitable back-lash from some folks. I would just say - TRY ONE. If you don't fall in love with this calibre, you probably don't actually have a heart, but simply a half-brick on a piece of string, swinging from side to side. My experience with it in the field is NIL. But, I loosed off at the range over a morning, and it's a revelation.
My Sako 75 Hunter has arrived, and it feels absolutely RIGHT. Now, others may know what I mean here. It feels as if it has always been with me: almost an extension of my arm. If it shoots straight, and kills as cleanly as I'm sure it will, then this will be MY rifle, and MY calibre for the rest of my stalking days.
Changing rifles is like changing wives: expensive, and uncertain. Try the shortlist at the range, and choose something you can love. That's it, and all about it.