Ethernet splicing advice

I'm moving into a house that has ethernet running to each room which originates from a closet and I'd like to extend these existing cables to reach another room where all other equipment will be.

So, my question is regarding splicing to the existing cables and wanting to maintain the best quality and speed.
Would you expect to have a better connection using a small patch panel to the existing cables (that already have RJ45 ends) or cutting the ends and using a junction box?

Or another option I've not considered.