Monogatari series and Oregairu have one major thing in common. Characters.
Character development and character interaction are the essences of these two brilliant anime. These are the two main reasons that I enjoy both series so much. The gradual change in character, the interactions that thread word play and philosophy through them and just the overall brilliance of the writing.
First of all, the main character (Hachiman and Koyomi).
Both male, both have ahoges, both have sisters etc.
However, the main connection between the two is the fact that they will try and save everyone else, even at the cost of himself.
The female leads (Yukino and Hitagi) are also very interesting characters.
Through various situations, they become closer to the main character. They are strong and independent females that seem to be cut off from the rest of world. Yukino was cut off from society due to her beauty, Hitagi isolated herself due to her "disease".
Both of them enjoy making fun of the mc, however there are definitely positive feelings towards each respective mc.
Another similarity between the two is the setting.
Common in the world of anime, these series are both set in high school where youth is at it's height. Worries of a high school student such as friendship, love and graduation.
Family situations play quite a large part in these two.
Every character has a different family situation and these family situations have quite a large effect on each story line.
On to music.
MONACA (a music production studio) produced the beautiful OSTs for both of these anime series.
Nagi Yanagi has also sung for both series. In Bakemonogatari, she worked with supercell as the guest vocalist for "Kimi no Shiranai Monogatar" (Bakemonogatari ED). In Oregairu, she produced the singles for both seasons: "Yukitoki" (S1 OP) and "Harumodoki" (Zoku's OP).
Last of all, voice actors and their acting.
I believe that each and every single character in both of these shows has the perfect voice actor/actress. The voice acting for the characters is perfect.
I thoroughly enjoy both series and I re-watch both series nearly on a daily basis.