Sir John and Colonel Brandon were of contrasting temperments. One is merry and gregarious, the other is quiet and serious.

I didn't know the flannel waistcoat could signify the Colonel was also a sportsman ! They may've spent a fair bit of time in each other's company.
Although Brandon may've was quiet, he was probably glad to accept invitations to Barton Park for company and found himself well received.
Sir John would be glad to see his friend to chat about sport.
Lady Middleton likely approved Col. Brandon's genteel manner- Lady M. seems a different sort of person to her husband, so it's interesting if Brandon was able to get along well with them both.
Also Mrs Jennings must find him of interest if she is anxious to see him well married.
They appear of contrasting temperments yet have common interests.
Sir John's family also liked Col. Brandon so he was welcome at their home.